400puzzles Problem Set

8/13/2019 400puzzles Problem Set

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Three friends divided some bullets equally. After all of them shot 4 bullets the total number of bullets remaining is equal tothe bullets each had after division. Find the original number divided.

Answer

18

Assume that initial there were 3*X bullets.

So they got X bullets each after division.

All of them shot 4 bullets. So now they have X ! 4" bullets each.

#ut it is given that$after they shot 4 bullets each$ total number of bullets remaining is equal to the bullets each had afterdivision i.e. X

Therefore$ the equation is3 * X ! 4" % X3 * X ! &' % X' * X % &'X % (

Therefore the total bullets before division is % 3 * X % &)

Find sum of digits of .

+etA% &,,,&,,,# % sum of digits of A- % sum of digits of # % sum of digits of -

/0T 1 A % # % - % mod ,""

Answer

The sum of the digits od D is 1.

+et 2 % sum of digits of .

/t follows from the hint that A % 2 mod ,"


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Consider,

A = 19991999

< 20002000

= 22000* 10002000

= 1024

200

* 10

6000

< 10800* 106000

= 106800

i.e. A < 106800

i.e. B < 6800 * 9 = 61200

i.e. C < 5 * 9 = 45

i.e. D < 2 * 9 = 18

i.e. E


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0ote that at first glance$ one might thin that the total distance covered by the last erson is &77 meters$ as he ran thetotal lenght of the latoon 67 meters" twice. T=>2$ but that5s the relative distance covered by the last erson i.e.assuming that the latoon is stationary.

/f you tae a marer ? start from a corner on a cube$ what is the ma@imum number of edges you can trace across if younever trace across the same edge twice$ never remove the marer from the cube$ ? never trace anywhere on the cube$

e@cet for the corners ? edges

Answer

9

To verify this$ you can mae a drawing of a cube$ ? number each of its &' edges. Then$ always starting from & corner ? &edge$ you can determine all of the ossible combinations for tracing along the edges of a cube.

There is no need to start from other corners or edges of the cube$ as you will only be reeating the same combinations.The rocess is a little more involved than this$ but is useful for solving many tyes of satial uBBles.

Cne of Dr. #aEaE$ his wife$ their son and Dr. #aEaE5s mother is an 2ngineer and another is a octor.

/f the octor is a male$ then the 2ngineer is a male.

/f the 2ngineer is younger than the octor$ then the 2ngineer and the octor are not blood relatives.

/f the 2ngineer is a female$ then she and the octor are blood relatives.

-an you tell who is the octor and the 2ngineerAnswer

Mr. a!a! is the "ngineer and either his wife or his son is the Doctor.

Dr. #aEaE5s wife and mother are not blood relatives. So from 3$ if the 2ngineer is a female$ the octor is a male. #ut from &$if the octor is a male$ then the 2ngineer is a male. Thus$ there is a contradiction$ if the 2ngineer is a female. ence$either Dr. #aEaE or his son is the 2ngineer.

Dr. #aEaE5s son is the youngest of all four and is blood relative of each of them. So from '$ Dr. #aEaE5s son is not the2ngineer. ence$ Dr. #aEaE is the 2ngineer.

0ow from '$ Dr. #aEaE5s mother can not be the octor. So the octor is either his wife or his son . /t is not ossible todetermine anything further.

Three men ! Sam$ -am and +aurie ! are married to -arrie$ #illy and Tina$ but not necessarily in the same order.

Sam5s wife and #illy5s usband lay -arrie and Tina5s husband at bridge. 0o wife artners her husband and -am doesnot lay bridge.

ho is married to -am

Answer

#arrie is married to #am.

GSam5s wife and #illy5s usband lay -arrie and Tina5s husband at bridge.G

/t means that Sam is not married to either #illy or -arrie. Thus$ Sam is married to Tina.

As -am does not lay bridge$ #illy5s husband must be +aurie.

ence$ -arrie is married to -am.

There are 3 ersons X$ H and I. Cn some day$ X lent tractors to H and I as many as they had. After a month H gave asmany tractors to X and I as many as they have. After a month I did the same thing. At the end of this transaction each


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one of them had '4.

Find the tractors each originally had

Answer

Cne way to solve it is by maing 3 equations and solve them simultaneously. #ut there is rather easier way to solve itusing #actracing.

/t5s given that at the end$ each had '4 tractors '4$ '4$ '4" i.e. after I gave tractors to X ? H as many as they had. /tmeans that after getting tractors from I their tractors got doubled. So before I gave them tractors$ they had &' tractorseach and I had 4) tractors. &'$ &'$ 4)"

Similarly$ before H gave tractors to X ? I$ they had ( ? '4 tractors resectively and H had 4' tractors i.e. ($ 4'$ '4"

Again$ before X gave tractors to H ? I$ they had '& ? &' tractors resectively and X had 3, tractors i.e. 3,$ '&$ &'"

ence$ initially $ had %9 tractors& ' had 21 tractors and( had 12 tractors.

A certain street has &777 buildings. A sign!maer is contracted to number the houses from & to &777. ow many Beroeswill he need

Answer

The sign)ma*er will need 192 +eroes.

ivide &777 building numbers into grous of &77 each as follow1&..&77"$ &7&..'77"$ '7&..377"$ ....... ,7&..&777"

For the first grou$ sign!maer will need && Beroes.For grou numbers ' to ,$ he will require '7 Beroes each.And for grou number &7$ he will require '& Beroes.

The total numbers of Beroes required are% && 8 )*'7 8 '&% && 8 &(7 8 '&% &,'

There are , coins. Cut of which one is odd one i.e weight is less or more. ow many iterations ofweighing are required to find odd coin

Answer

/t is always ossible to find odd coin in 3 weighings and to tell whether the odd coin is heavier orlighter.

&. Tae ) coins and weigh 4 against 4.o /f both are not equal$ goto ste 'o /f both are equal$ goto ste 3

'. Cne of these ) coins is the odd one. 0ame the coins on heavier side of the scale as &$'$ 3 and 4. Similarly$ name the coins on the lighter side of the scale as +&$ +'$ +3and +4. 2ither one of 5s is heavier or one of +5s is lighter. eigh &$ '$ +&" against3$ 4$ X" where X is one coin remaining in intial weighing.

o /f both are equal$ one of +'$ +3$ +4 is lighter. eigh +' against +3.

/f both are equal$ +4 is the odd coin and is lighter. /f +' is light$ +' is the odd coin and is lighter.


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on for the nine digits of the number i.e. the number formed from the first n digits isdivisible by n$ 'L%nL%,.

2ach digit in the number is different i.e. no digits are reeated.

The digit 7 does not occur in the number i.e. it is comrised only of the digits &!, in someorder.

Find the number.

Answer

The answer is %81,/729

Cne way to solve it is Trial!?!2rror. Hou can mae it bit easier as odd ositions will always occuyC numbers and even ositions will always occuy 2M20 numbers. Further 6th osition willcontain 6 as 7 does not occur.

The other way to solve this roblem is by writing a comuter rogram that systematically tries allossibilities

&;3 rd of the contents of a container evaorated on the &st day. 3;4th of the remaining contents of thecontainer evaorated on the second day.

hat art of the contents of the container is left at the end of the second day

Answer

Assume that contents of the container is X

Cn the first day &;3rd is evaorated.& ! &;3" of X is remaining i.e. ';3"X

Cn the Second day 3;4th is evaorated. ence$&! 3;4" of ';3"X is remainingi.e. &;4"';3"X % &;(" X

ence &;(th of the contents of the container is remaining

Miul was studying for his e@aminations and the lights went off. /t was around &177 AD. e lightedtwo uniform candles of equal length but one thicer than the other. The thic candle is suosedto last si@ hours and the thin one two hours less. hen he finally went to slee$ the thic candlewas twice as long as the thin one.

For how long did Miul study in candle light

Answer

ipul studied for % hours in candle light.

Assume that the initial lenght of both the candle was + and Miul studied for X hours.

/n X hours$ total thic candle burnt % X+;(/n X hours$ total thin candle burnt % X+;4


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After X hours$ total thic candle remaining % + ! X+;(After X hours$ total thin candle remaining % + ! X+;4

Also$ it is given that the thic candle was twice as long as the thin one when he finally went toslee.+ ! X+;(" % '+ ! X+;4"( ! X";( % 4 ! X";'( ! X" % 3*4 ! X"( ! X % &' ! 3X'X % (X % 3

ence$ Miul studied for 3 hours i.e. &)7 minutes in candle light.

/f you started a business in which you earned =s.& on the first day$ =s.3 on the second day$ =s.6on the third day$ =s.< on the fourth day$ ? so on.

ow much would you have earned with this business after 67 years assuming there are e@actly3(6 days in every year"

Answer

s.%%%&0,2&00

To begin with$ you want to now the total number of days1 3(6 @ 67 % &)'67.

#y e@erimentation$ the following formula can be discovered$ ? used to determine the amountearned for any articular day1 & 8 '@!&"$ with @ being the number of the day. Tae half of the&)'67 days$ ? air them u with the other half in the following way1 day & with day &)'67$ day 'with day &)'4,$ ? so on$ ? you will see that if you add these airs together$ they always equal=s.3(677.

Dultily this number by the total number of airs ,&'6"$ ? you have the amount you would haveearned in 67 years.

Dath gurus may use series formula to solve it.series1 &$3$6$


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at &'5o.

Answer

,, seconds

/t is given that the time between first and last tics at (5o is 37 seconds.Total time gas between first and last tics at (5o % 6i.e. between & ? '$ ' ? 3$ 3 ? 4$ 4 ? 6 and 6 ? ("

So time ga between two tics % 37;6 % ( seconds.

0ow$ total time gas between first and last tics at &'5o % &&Therefore time taen for &' tics % && * ( % (( seconds and not (7 seconds"

677 men are arranged in an array of &7 rows and 67 columns according to their heights.

Tallest among each row of all are ased to come out. And the shortest among them is A.

Similarly after resuming them to their original ositions$ the shortest among each column areased to come out. And the tallest among them is #.

0ow who is taller A or # Answer

o one is taller& 3oth are same as A and are the same person.

As it is mentioned that 677 men are arranged in an array of &7 rows and 67 columns accordingto their heights. +et5s assume that osition numbers reresent their heights. ence$ the shortestamong the 67$ &77$ &67$ ... 467$ 677 is erson with height 67 i.e. A. Similarly the tallest among &$'$ 3$ 4$ 6$ ..... 4)$ 4)$ 67 is erson with height 67 i.e. #

0ow$ both A and # are the erson with height 67. ence both are same.

/n Dr. Dehta5s family$ there are one grandfather$ one grandmother$ two fathers$ two mothers$ onefather!in!law$ one mother!in!law$ four children$ three grandchildren$ one brother$ two sisters$ twosons$ two daughters and one daughter!in!law.

ow many members are there in Dr. Dehta5s family Oive minimal ossible answer.


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Answer

There are < members in Dr. Dehta5s family. Dother ? Father of Dr. Dehta$ Dr. ? Drs. Dehta$ hisson and two daughters.

Dother ? Father of Dr. DehtaPP

Dr. ? Drs. DehtaPP

Cne Son ? Two aughtershen Ale@ander the Oreat attaced the forces of Qorus$ an /ndian soldier was catured by theOrees. e had dislayed such bravery in battle$ however$ that the enemy offered to let himchoose how he wanted to be illed. They told him$ G/f you tell a lie$ you will ut to the sword$ and ifyou tell the truth you will be hanged.G

The soldier could mae only one statement. e made that statement and went free. hat did hesay

Answer

The soldier said$ GHou will ut me to the sword.G

The soldier has to say a Qarado@ to save himself. /f his statement is true$ he will be hanged$which is not the sword and hence false. /f his statement is false$ he will be ut to the sword$ whichwill mae it true. A Qarado@ RRR

A erson wanted to withdraw X ruees and H aise from the ban. #ut cashier made a mistaeand gave him H ruees and X aise. 0either the erson nor the cashier noticed that.

After sending '7 aise$ the erson counts the money. And to his surrise$ he has double theamount he wanted to withdraw.

Find X and H. & =uee % &77 Qaise"


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Answer

As given$ the erson wanted to withdraw &77X 8 H aise.

#ut he got &77H 8 X aise.

After sending '7 aise$ he has double the amount he wanted to withdraw. ence$ theequation is

2 * "100$ % = 100& % $ ' 20

200$ % 2& = 100& %$ ' 20

199$ ' 98& = '20

98& ' 199$ = 20

0ow$ we got one equationK but there are ' variables. e have to aly little bit of logic over

here. e now that if we interchange X ? H$ amount gets double. So H should be twice of X orone more than twice of X i.e. H % 'X or H % 'X8&

-ase / 1'42$Solving two equations simultaneously,)H ! &,,X % '7H ! 'X % 7e get X % ! '7;3 ? H % ! 47;'

-ase // 1'42$51Solving two equations simultaneously,)H ! &,,X % '7H ! 'X % &

e get X % '( ? H % 63

0ow$ its obvious that he wanted to withdraw =s. '(.63

SubmitAnswer

UsersAnswer (2)

BrainVistaAnswer

The game of Tic!Tac!Toe is being layed between two layers. Cnly the last mar to be laced inthe game as shown.

ho will win the game$ C or X -an you tell which was the si@th mar and at which osition oe@lain your answer.

At the Qarty1

&. There were , men and children.'. There were ' more women than children.3. The number of different man!woman coules ossible was '4. 0ote that if there were 4,& (47& "48& D49

/t is obvious that >%& as >*ST2D%ST2D" and -%7 as /!-%/".

S*C is a single digit and also S*T is a single digit. ence$ their values C$ S$ T" must be '$ 3 or 4

as they can not be 7 or & or greater than 4".

-onsider$ ST2D*C%DC-$ where -%7. /t means that D must be 6. 0ow$ its simle. C%4$ S%'$T%3$ 2%)$ I%


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( ) 4 1

''''''''''''' '''''''''''''

+ E - D E + E 2 8 5 - 9 8 5 6 2 8

- D ( C - 9 5 4 0

''''''''''''' '''''''''''''

) + 1 6 2

+ E 2 8 5

'''''''''' ''''''''''

/ / / E 8

/ ) 1 5 5

'''''''' ''''''''

+ 6 2

Also$ when arranged from 7 to ,$ it sells #=T6M>("D.At what time after 4.77 .m. is the minutes hand of a cloc e@actly aligned with the hour hand

Answer

/?21?/9.

Assume that X minutes after 4.77 QD minute hand e@actly aligns with and hour hand.

For every minute$ minute hand travels ( degrees.

ence$ for X minutes it will travel ( * X degrees.

For every minute$ hour hand travels &;' degrees.ence$ for X minutes it will travel X;' degrees.

At 4.77 QD$ the angle between minute hand and hour hand is &'7 degrees. Also$ after X minutes$minute hand and hour hand are e@actly aligned. So the angle with resect to &' i.e. Mertical Qlanewill be same. Therefore$

( * X % &'7 8 X;'&' * X % '47 8 X&& * X % '47X % '&.)&)'X % '& minutes 4,.6 seconds

ence$ at 41'&14,.6 minute hand is e@actly aligned with the hour hand.

A soldier looses his way in a thic Eungle. At random he wals from his cam but mathematicallyin an interesting fashion.

First he wals one mile 2ast then half mile to 0orth. Then &;4 mile to est$ then &;) mile to Southand so on maing a loo.


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Finally how far he is from his cam and in which direction

Answer

The soldier is 0.89// miles awa- from his camp towards "ast)orth.

/t is obvious that he is in 2ast!0orth direction.

istance travelled in 0orth and South directions% &;' ! &;) 8 &;3' ! &;&') 8 &;6&' ! &;'74) 8 and so on... a geometric series with r % !&;4" "

&;'" * & ! !&;4"n"% !!!!!!!!!!!!!!!!!!!!!!!!!!!

& ! !&;4" "

% & ; ' * & ! !&;4" " "% ';6

Similarly in 2ast and est directions

% & ! &;4 8 &;&( ! &;(4 8 &;'6( ! and so on... a geometric series with r % !&;4" "

&" * & ! !&;4"n"% !!!!!!!!!!!!!!!!!!!!!!!!!!!

& ! !&;4" "

% & ; &! !&;4" "% 4;6

So the soldier is 4;6 miles away towards 2ast and ';6 miles away towards 0orth. So using rightangled triangle$ soldier is 7.),44 miles away from his cam.

=aE has a Eewel chest containing =ings$ Qins and 2ar!rings. The chest contains '( ieces. =aE

has ' &;' times as many rings as ins$ and the number of airs of earrings is 4 less than thenumber of rings.

ow many earrings does =aE have

Answer

12 earrings

Assume that there are = rings$ Q ins and 2 air of ear!rings.

/t is given that$ he has ' &;' times as many rings as ins.= % 6;'" * Q or Q % '*=";6

And$ the number of airs of earrings is 4 less than the number of rings.2 % = ! 4 or = % 2 8 4

Also$ there are total '( ieces.= 8 Q 8 '*2 % '(= 8 '*=";6 8 '*2 % '(6*= 8 '*= 8 &7*2 % &37


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Answer

20 cows

g ! grass at the beginningr ! rate at which grass grows$ er dayy ! rate at which one cow eats grass$ er dayn ! no of cows to eat the grass in ,( days

From given data$g 8 '4*r %


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The last digit can not be 7.

/f the last digit is &$ the only ossible number is &7&. 0ote that 7&& is not a 3!digit number"

/f the last digit is '$ the ossible numbers are '7' and &&'.

/f the last digit is 3$ the ossible numbers are 373$ '&3 and &'3.

/f the last digit is 4$ the ossible numbers are 474$ 3&4$ ''4 and &34.

/f the last digit is 6$ the ossible numbers are 676$ 4&6$ 3'6$ '36 and &46.

0ote the attern here ! /f the last digit is &$ there is only one number. /f the last digit is '$ there aretwo numbers. /f the last digit is 3$ there are three numbers. /f the last digit is 4$ there are fournumbers. /f the last digit is 6$ there are five numbers. And so on.....

Thus$ total numbers are& 8 ' 8 3 8 4 8 6 8 ( 8 < 8 ) 8 , % 46

Altogether then$ there are 46 different 3!digit numbers$ where last digit is the sum of first two

digits.

Find the smallest number such that if its rightmost digit is laced at its left end$ the new numberso formed is recisely 67N larger than the original number.Answer

The answer is 2871/.

/f its rightmost digit is laced at its left end$ then new number is 4')6


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0ow adding both the robability$ the required robability is% ' ; 6& * 63" 8 67 ; 6& * 63"% 6' ; 6& * 63"% 6' ; '


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Answer

There are total ) such series1

&. Sum of '777 numbers starting from !,,, i.e. summation of numbers from !,,, to &777.

!,,," 8 !,,)" 8 !,,


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ow many for a 4@4@4 cubeSubmitted

Answer

There are /.%22 C 1019 possi3le com3inations for %%% u3ics and 7./012 C 10/possi3le com3inations for /// u3ics.

+et5s consider 3@3@3 =ubics first.

There are ) corner cubes$ which can be arranged in )R ways.2ach of these ) cubes can be turned in 3 different directions$ so there are 3W) orientationsaltogether. #ut if you get all but one of the corner cube into chosen ositions and orientations$only one of 3 orientations of the final corner cube is ossible. Thus$ total ways corner cubes canbe laced % )R" * 3W)";) % )R" * 3W


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Answer

A tough oneRRR

Since = 8 2 8 2 % &7 8 2$ it is clear that = 8 2 % &7 and neither = nor 2 is equal to 7 or 6. This isthe only entry oint to

solve it. 0ow use trial!n!error method.

E 3 E 2 1 4 1 9

E A 3 E 1 5 4 1

% E % 6 1

''''''''''''''''' '''''''''''''''''

A ( E 5 0 2 1

Cne of the four eole ! Dr. -linton$ his wife Donia$ their son Dandy and their daughter -indy !is a singer and another is a dancer. Dr. -linton is older than his wife and Dady is older than hissister.

&. /f the singer and the dancer are the same se@$ then the dancer is older than the singer.'. /f neither the singer nor the dancer is the arent of the other$ then the singer is older than

the dancer.3. /f the singer is a man$ then the singer and the dancer are the same age.4. /f the singer and the dancer are of oosite se@ then the man is older than the woman.6. /f the dancer is a woman$ then the dancer is older than the singer.

hose occuation do you now And what is his;her occuation

Answer

#ind- is the inger. Mr. #linton or Moni*a is the Dancer.

From &" and 3"$ the singer and the dancer$ both can not be a man. From 3" and 4"$ if the singeris a man$ then the dancer must be a man. ence$ the singer must be a woman.

#A" >1 Singer is a woman and ancer is also a womanThen$ the dancer is Donia and the singer is -indy.

#A" >>1 Singer is a woman and ancer is also a manThen$ the dancer is Dr. -linton and the singer is -indy.

/n both the cases$ we now that -indy is the Singer. And either Dr. -linton or Donia is theancer.There are '7 eole in your alicant ool$ including 6 airs of identical twins.

/f you hire 6 eole randomly$ what are the chances you will hire at least & air of identical twins0eedless to say$ this could cause trouble K""Submitted

Answer


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The pro3a3ilit- to hire people with at least 1 pair of identical twins is 2.28


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Thus$ total distance covered by the last erson% 678X" 8 X% '*X 8 67% '*36.366" 8 67% &'7.


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The rogram should outut all the ossible values of A$ #$ -$ and 2 for which the equation issatisfied.

/n a =oad =ace$ one of the three biers was doing &6m less than the first and 3m more thanthe third. e also finished the race &' minutes after the first and 3 minutes before the third.

-an you find out the seed of each bier$ the time taen by each bier to finish the race and thelength of the course

Assume that there were no stos in the race and also they were driving with constant seedsthrough out the

Answer

+et us assume thatSeed of First bier % M& m;minSeed of Second bier % M' m;minSeed of Third bier % M3 m;minTotal time tae by first bier % T& minTotal distance % S m

0ow as er the data given in the teaser$ at a time T min $1 = 31 * '''' 1

$1 ' 15 = 32 * '''' 2

$1 ' 18 = 3 * ''''

At a istance S m. + = 31 * 1 '''' 4

+ = 32 * "1 % 12# '''' 5

+ = 3 * "1 % 15# '''' 6

Thus there are ( equations and < unnown data that means it has infinite number of solutions.


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between #holu5s and olu5s age is < years.

ence$ the ma@imum ossible value of the sum of the difference in their ages ! taen two at atime ! is ' 8 6 8


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Thus$ first two digits must be either ' or 3 i.e. ''$ '3$ 3' or 33 which means that there are fourossible numbers ! ''4$ '3($ 3'( and 33,.

0ow$ it is also given that ! the difference between it5s reverse and itself is 3,(. Cnly '3( satisfiesthis condition. ence$ the sum of the three digits is &&.

There are 4 mugs laced uturned on the table. 2ach mug have the same number of marblesand a statement about the number of marbles in it. The statements are1 Two or Three$ Cne orFour$ Three or Cne$ Cne or Two.

Cnly one of the statement is correct. ow many marbles are there under each mug

Answer

A simle one.

As it is given that only one of the four statement is correct$ the correct number can not aear inmore than one statement. /f it aears in more than one statement$ then more than onestatement will be correct.

ence$ there are 4 marbles under each mug.At >niversity of Qrobability$ there are 3

0ote that 7&'346( may not be a valid

An anthroologist discovers an isolated tribe whose written alhabet contains only si@ letters callthe letters A$ #$ -$ $ 2 and F". The tribe has a taboo against using the same letter twice in thesame word. /t5s never done.

/f each different sequence of letters constitues a different word in the language$ what is the


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ma@imum number of si@!letter words that the language can emloySubmitted

Answer

The language can emplo- maimum of 720 si)letter words.

/t is a simle ermutation roblem of arranging ( letters to get different si@!letter words. And it canbe done in in (R ways i.e.


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Answer

A tricy C02.

Oiven 3 oints are colinear. ence$ it is a straight line.

ence area of triangle is 7.

Silu and Deenu were waling on the road.

Silu said$ G/ weigh 6& gs. ow much do you weighG

Deenu relied that she wouldn5t reveal her weight directly as she is overweight. #ut she said$ G/weigh ', gs lus half of my weight.G

ow much does Deenu weigh

Answer

Meenu weighs 8 Fgs.

/t is given that Deenu weighs ', gs lus half of her own weight. /t means that ', gs is theother half. So she weighs 6) gs.

Solving mathematically$ let5s assume that her weight is X gs.X % ', 8 X;''*X % 6) 8 XX % 6) gs

-onsider the sum1 A#- 8 2F 8 O/ %

/f different letters reresent different digits$ and there are no leading Beros$ what does reresent

Answer

The value of G must 3e 9.

Since there are no leading Beros$ must be


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Answer

The answer is simle. /t says the man wants to fit GTen orsesG into nine stables. There are nineletters in the hrase GTen orsesG. So you can ut one letter each in all nine stables. 7 7E 7 7 7( 7 7+ 7E 7+

A man is at a river with a , gallon bucet and a 4 gallon bucet. e needs e@actly ( gallons ofwater.

ow can he use both bucets to get e@actly ( gallons of water

0ote that he cannot estimate by duming some of the water out of the , gallon bucet or the 4gallon bucetAnswer

For the sac of e@lanation$ let5s identify 4 gallon bucet as #ucet Q and , gallon bucet as#ucet .

6peration

/ gallon 3uc*et:uc*et E;

9 gallon 3uc*et:uc*et H;

/nitially 7 7

Fill the bucet with , gallon water 7 ,

Qour 4 gallon water from bucet to bucet Q 4 6

2mty bucet Q 7 6

Qour 4 gallon water from bucet to bucet Q 4 &

2mty bucet Q 7 &

Qour & gallon water from bucet to bucet Q & 7

Fill the bucet with , gallon water & ,

Qour 3 gallon water from bucet to bucet Q 4 (

, gallon bucet contains ( gallon of water$ as required.

2ach of the five characters in the word #=A/0 has a different value between 7 and ,. >sing thegiven grid$ can you find out the value of each character B A 1

B B B A 1

A B B 2

B A 0

A A A 2

29 25 2 29

The numbers on the e@treme right reresent the sum of the values reresented by the charactersin that row. Also$ the numbers on the last raw reresent the sum of the values reresented by thecharacters in that column. e.g. # 8 = 8 A 8 / 8 0 % 3& from first row"


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Answer

47& 4,& A4/& >4 and 49

Dae total &7 equations ! 6 for rows and 6 for columns ! and sovle them.

From =ow3 and =ow4$0 8 / 8 A 8 # 8 # % 0 8 / 8 # 8 A 8 / 8 '# % / 8 '

From =ow& and =ow3$# 8 = 8 A 8 / 8 0 % 0 8 / 8 A 8 # 8 # ! &= % # ! &

From -olumn'$= 8 # 8 / 8 / 8 = % ',# 8 '= 8 '/ % ',# 8 '# ! &" 8 '/ % ',3# 8 '/ % 3&

3/ 8 '" 8 '/ % 3&6/ % '6/ % 6

ence$ #%< and =%(

From =ow'$# 8 # 8 = 8 # 8 A % 3&3# 8 = 8 A % 3&3


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'. Cne of these ) coins is the odd one. 0ame the coins on heavier side of the scale as &$'$ 3 and 4. Similarly$ name the coins on the lighter side of the scale as +&$ +'$ +3and +4. 2ither one of 5s is heavier or one of +5s is lighter. eigh &$ '$ +&" against3$ 4$ X" where X is one coin remaining in intial weighing.

o /f both are equal$ one of +'$ +3$ +4 is lighter. eigh +' against +3.

/f both are equal$ +4 is the odd coin and is lighter. /f +' is light$ +' is the odd coin and is lighter. /f +3 is light$ +3 is the odd coin and is lighter.

o /f &$ '$ +&" is heavier side on the scale$ either & or ' is heavier. eight &against '

/f both are equal$ there is some error. /f & is heavy$ & is the odd coin and is heavier. /f ' is heavy$ ' is the odd coin and is heavier.

o /f 3$ 4$ X" is heavier side on the scale$ either 3 or 4 is heavier or +& islighter. eight 3 against 4

/f both are equal$ +& is the odd coin and is lighter. /f 3 is heavy$ 3 is the odd coin and is heavier. /f 4 is heavy$ 4 is the odd coin and is heavier.

3. The remaining coin X is the odd one. eigh X against the anyone coin used in initialweighing.

o /f both are equal$ there is some error.

o /f X is heavy$ X is the odd coin and is heavier.o /f X is light$ X is the odd coin and is lighter.

/n a sorts contest there were m medals awarded on n successive days n J &".

&. Cn the first day & medal and &;< of the remaining m ! & medals were awarded.'. Cn the second day ' medals and &;< of the now remaining medals was awardedK and so

on.

!. Cn the nthand last day$ the remaining n medals were awarded.

ow many days did the contest last$ and how many medals were awarded altogetherAnswer

Total %, medals were awarded and the contest was for , da-s.

Cn day &1 Dedals awarded % & 8 36;


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/ got this answer by writing small rogram. /f anyone now any other simler method$ do submit it.

A number of , digits has the following roerties1

The number comrising the leftmost two digits is divisible by '$ that comrising the

leftmost three digits is divisible by 3$ the leftmost four by 4$ the leftmost five by 6$ and soon for the nine digits of the number i.e. the number formed from the first n digits isdivisible by n$ 'L%nL%,.

2ach digit in the number is different i.e. no digits are reeated.

The digit 7 does not occur in the number i.e. it is comrised only of the digits &!, in someorder.

Find the number.

Answer

The answer is %81,/729

Cne way to solve it is Trial!?!2rror. Hou can mae it bit easier as odd ositions will always occuyC numbers and even ositions will always occuy 2M20 numbers. Further 6th osition willcontain 6 as 7 does not occur.

The other way to solve this roblem is by writing a comuter rogram that systematically tries allossibilities.

&;3 rd of the contents of a container evaorated on the &st day. 3;4th of the remaining contents ofthe container evaorated on the second day.

hat art of the contents of the container is left at the end of the second dayAnswer

Assume that contents of the container is X

Cn the first day &;3rd is evaorated.& ! &;3" of X is remaining i.e. ';3"X

Cn the Second day 3;4th is evaorated. ence$&! 3;4" of ';3"X is remainingi.e. &;4"';3"X % &;(" X

ence &;(th of the contents of the container is remaining

There are four eole in a room not including you". 2@actly two of these four always tell the truth.The other two always lie.

Hou have to figure out who is who /0 C0+H ' >2ST/C0S. Hour questions have to be H2S or0C questions and can only be answered by one erson. /f you as the same question to twodifferent eole then that counts as two questions". ee in mind that all four now each other5scharacteristics whether they lie or not.

hat questions would you as to figure out who is who =emember that you can as only 'questions.Submitted


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Hou have 3 basets$ ? each one contains e@actly 4 balls$ each of which is of the same siBe. 2achball is either red$ blac$ white$ or urle$ ? there is one of each color in each baset.

/f you were blindfolded$ ? lightly shoo each baset so that the balls would be randomlydistributed$ ? then too & ball from each baset$ what chance is there that you would have e@actly' red balls

Answer

There are (4 different ossible outcomes$ ? in , of these$ e@actly ' of the balls will be red. Thereis thus a slightly better than &4N chance 9,;(4"*&77: that e@actly ' balls will be red.

A much faster way to solve the roblem is to loo at it this way. There are 3 scenarios wheree@actly 3 balls are red1

1 2

'''''''''''

$

$

$

$ is an: !all t;at is not red.

There is a 4.()


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Answer

The robability of winning the lottery is two in one billion i.e. only two erson can win from onebillion RRR

+et5s find out samle sace first. The +ottery -ommission chooses && numbers from the )7.ence$ the && numbers from the )7 can be selected in )7-&&ways which is very very high and isequal to &.74


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A =oo and a #isho on a standard chess!board can be arranged in (4Q'% (4*(3 % 473' ways

0ow$ there are ' cases ! =oo attacing #isho and #isho attacing =oo. 0ote that the =ooand the #isho never attac each other simultaneously. +et5s consider both the cases one by one.

#ase > ) oo* attac*ing ishopThe =oo can be laced in any of the given (4 ositions and it always attacs &4 ositions.ence$ total ossible ways of the =oo attacing the #isho % (4*&4 % ),( ways

#ase >> ) ishop attac*ing oo*Miew the chess!board as a 4 co!centric hollow squares with the outermost square with side )units and the innermost square with side ' units.

/f the bisho is in one of the outer ') squares$ then it can attac < ositions. /f the bisho is in oneof the '7 squares at ne@t inner!level$ then it can attac , ositions. Similarly if the bisho is in oneof the &' squares at ne@t inner!level$ then it can attac && ositions. And if the bisho is in one ofthe 4 squares at ne@t inner!level the innermost level"$ then it can attac &3 ositions.

ence$ total ossible ways of the #isho attacing the =oo

% ')*< 8 '7*, 8 &'*&& 8 4*&3% 6(7 ways

Thus$ the required robability is% ),( 8 6(7" ; 473'% &3;3(% 7.3(&&itted ed

ere in 2ngland Dconald5s has Eust launched a new advertising camaign. The oster shows )Dconald5s roducts and underneath claims there are 473&' combinations of the above items.

Oiven that the ma@imum number of items allowed is )$ and you are allowed to have less than )items$ and that the order of urchase does not matter i.e. buying a burger and fries is the same

as buying fries and a burger"

ow many ossible combinations are there Are Dconald5s correct in claiming there are 473&'combinationsAnswer

Total possi3le com3inations are 128,9.

/t is given that you can order ma@imum of ) items and you are allowed to have less than ) items.Also$ the order of urchase does not matter. +et5s create a table for ordering total 0 items using Xroducts.

>tems

6rdered:;

Eroducts =sed :$;

& ' 3 4 6 ( < )

& & ! ! ! ! ! ! !

' & & ! ! ! ! ! !

3 & ' & ! ! ! ! !


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4 & 3 3 & ! ! ! !

6 & 4 ( 4 & ! ! !

( & 6 &7 &7 6 & ! !

< & ( &6 '7 &6 ( & !

) & < '& 36 36 '& < &

Total :T; ) ') 6(


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/n one minute$ie A can fill &;37 art of the tan.ie # can fill &;'4 art of the tan.

Thus$ the net water level increase in one minute is% &;37 8 &;'4% 3;47 art of the tan

/n order to ee the tan always emty$ outlet ie - should emty at least 3;47 art of the tanin one minute. Thus$ ie - can emty the full tan in 47;3 i.e. &3 minutes '7 seconds.

A worer earns a 6N raise. A year later$ the worer receives a '.6N cut in ay$ ? now his salary is=s. ''


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As given$ the erson wanted to withdraw &77X 8 H aise.

#ut he got &77H 8 X aise.

After sending '7 aise$ he has double the amount he wanted to withdraw. ence$ theequation is

2 * "100$ % = 100& % $ ' 20

200$ % 2& = 100& %$ ' 20

199$ ' 98& = '20

98& ' 199$ = 20

0ow$ we got one equationK but there are ' variables. e have to aly little bit of logic overhere. e now that if we interchange X ? H$ amount gets double. So H should be twice of X orone more than twice of X i.e. H % 'X or H % 'X8&

-ase / 1'42$Solving two equations simultaneously,)H ! &,,X % '7H ! 'X % 7e get X % ! '7;3 ? H % ! 47;'

-ase // 1'42$51Solving two equations simultaneously,)H ! &,,X % '7H ! 'X % &e get X % '( ? H % 63

0ow$ its obvious that he wanted to withdraw =s. '(.63

SubmitAnswer

UsersAnswer (2)

BrainVistaAnswer

Puzzle

At the Qarty1

&. There were , men and children.'. There were ' more women than children.3. The number of different man!woman coules ossible was '4. 0ote that if there were %& as >*ST2D%ST2D" and -%7 as /!-%/".

S*C is a single digit and also S*T is a single digit. ence$ their values C$ S$ T" must be '$ 3 or 4as they can not be 7 or & or greater than 4".

-onsider$ ST2D*C%DC-$ where -%7. /t means that D must be 6. 0ow$ its simle. C%4$ S%'$T%3$ 2%)$ I%


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Answer

roup > costs s 120 and roup > costs s 1710

Assume that the values of one mango$ one ale and one banana are D$ A and # resectively.

From Orou // 1 D 8 6A 8


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/f GCG is laced in osition ($ GXG can always win by choosing osition 3$ 6 or


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Dr. agle goes to wor by a bus. Cne day he falls aslee when the bus still has twice as far to goas it has already gone.

alfway through the tri he waes u as the bus bounces over some bad otholes. hen hefinally falls aslee again$ the bus still has half the distance to go that it has already travelled.Fortunately$ Dr. agle waes u at the end of his tri.

hat ortion of the total tri did Dr. agle slee

Answer

Mr. wagle slept through half his trip.

+et5s draw a timeline. Qicture the bus route on a line showen below1

'''''''''''''''' ''''''''

+tart 1 12 2 End

''''' s;os tie or ;i; r. agle as not slee@ing

s;os tie or ;i; r. agle as slee@ing

3hen 4r. 3agle fell asleep the first time, the bus sill had twice as far to go as it hadalready gone, that marks the first third of his trip.

-e wake up halfway through the trip i.e slept from &! mark to the &( mark. -e fell sleepagain when the bus still had half the distance to go that it had already traveled i.e (!

mark.

dding up, all sleeping times,6 "&( + &!$ 7 "& + (!$6 &% 7 &!6 &(

-ence, 4r. wagle slept through half his trip.

Brain easer o 00068

/n your soc drawer$ you have a ratio of 6 airs of blue socs$ 4 airs of brown socs$ and (

airs of blac socs.

/n comlete darness$ how many socs would you need to ull out to get a matching air ofthe same color

//f you don5t agree$ try it yourselfRHou have a bucet of Eelly beans. Some are red$ some are blue$ and some green. ith your eyesclosed$ ic out ' of a lie color.


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ow many do you have to grab to be sure you have ' of the same

Hou have a bucet of Eelly beans. Some are red$ some are blue$ and some green. ith your eyesclosed$ ic out ' of a lie color.

ow many do you have to grab to be sure you have ' of the same/f you select 4 elly beans you are guarenteed that you will have ' that are the same color.

There are


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Assume that radius of the outer circle is = cmTherefore$' * Q/ * = % &')7777777 * Q/" 8 &' cm

Solving above equation$ = % (4777777&.,7) cm=adius of the earth is r % (47777777 cm

ence$ the thread will be searatedfrom the earth by% = ! r cm% (4777777&.,7) ! (47777777% &.,7) cmScientist decided to do a study on the oulation growth of rabbits. /nside a controlledenvironment$ &777 rabbits were laced.

Si@ months later$ there were &777I rabbits. At the beginning of the 3rd year$ there were roughly')')I rabbits$ which was 4 times what the scientists laced in there at the beginning of the &styear.

/f I is a ositive variable$ how many rabbits would be there at the beginning of the &&th yearSubmiAnswer

At the 3eginning of the 11th -ear& there would 3e 1&02/&000 ra33its.

At the beginning$ there were &777 rabbits. Also$ there were 4777 rabbits at the beginning of thirdyear which is equal to ')')I. Thus$ I % 4777;')') i.e. &.4&4 the square root of '"

0ote that ')')I can be reresented as '777*I*I I%&.4&4"$ which can be further simlified as&777*I*I*I*I

Also$ it is given that at the end of ( months$ there were &777I rabbits.

/t is clear that the oulation growth is &.4&4 times every si@ months i.e. ' times every year. After0 years$ the oulation would be &777*IW'0"" i.e. &777*'W0"

Thus$ at the beginning of the &&th year i.e. after &7 years"$ there would be &777*'W&7" i.e.&$7'4$777 rabbits.tted

A class of &77 students. '4 of them are girls and 3' are not. hich base am / using

Answer

+et the base be X.

ThereforeX*X 8 X*7 8 7" % '*X 84" 8 3*X 8 '"X*X % 6*X 8 (

X*X ! 6*X !( % 7X!("X8&" % 7

Therefore base is (

A man is stranded on a desert island. All he has to drin is a '7oB bottle of srite.

To conserve his drin he decides that on the first day he will drin one oB and the refill the bottlebac u with water. Cn the 'nd day he will drin 'oB and refill the bottle. Cn the 3rd day he will


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drin 3oB and so on...

#y the time all the srite is gone$ how much water has he drunSubmittAnswer

The man drun* 190o+ of water.

/t is given that the man has '7oB bottle of srite. Also$ he will drin &oB on the first day and refillthe bottle with water$ will drin 'oB on the second day and refill the bottle$ will drin 3oB on thethird day and refill the bottle$ and so on till '7th day. Thus at the end of '7 days$ he must havedrun & 8 ' 8 3 8 4 8 ..... 8&) 8 &, 8 '7" % '&7oB of liquid.

Cut of that '&7oB$ '7oB is the srite which he had initially. ence$ he must have drun &,7oB ofwater.edHou have four ,5s and you may use any of the 8$ !$ ;$ *" as many times as you lie. / want to see amathematical e@ression which uses the four ,5s to % &77

ow many such e@ressions can you maeSubmitted

Answer

There are 6 such e@ressions.

,, 8 ,;," % &77

,,;.,," % &77

,;.," * ,;.," % &77

,*," 8 ,";., % &77

,,!,";., % &77Two lanes tae off at the same e@act moment. They are flying across the Atlantic. Cne leaves

0ew Hor and is flying to Qaris at 677 miles er hour. The other leaves Qaris and is flying to 0ewHor at only 467 miles er hour because of a strong head wind ".

hich one will be closer to Qaris when they meetThey will both be the same distance from Qaris when they meetRRR

&' members were resent at a board meeting. 2ach member shoo hands with all of the othermembers before ? after the meeting.

ow many hand shaes were thereAnswer

1%2

Thin of it this way1 the first erson shaes hands with && eole$ the second erson also shaeshands with && eole$ but you only count &7$ because the hand shae with the first erson wasalready counted. Then add , for the third erson$ ) for the fourth$ ? so on.

(( hand shaes too lace before ? (( after the meeting$ for a total of &3'.Arrange five lanets such that 4 of them add u to 6th lanet numerically. 2ach of the letters ofthe lanet should reresent a unique number from the range 7 ! ,. Hou have to use all ten digits.

There is an amaBing mathematical relationshi e@ists among the names of the lanet.


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Answer

The tought rocess is initially to find lanets such that the total number of alhabets in them is &7.

The only ossible combination of lanets is Saturn$ >ranus$ Menus$ Dars and 0etune becausefor other combinations there will be more than &7 alhabets. Among these five$ 0etune is thelenghtiest$ so it must be the sum of the other four.

+ A )

) A ) +

3 E ) +

% A +

''''''''''''''

E F ) E

0ow the only ossible value for 0 is &. #y finding the value for S$ we can reach the result1

5 8 6 9 1

6 9 5 1 6

2 0 1 6

% 4 5 9

''''''''''''''

1 0 8 6 1 0

Hou have &4 ales. Hour Friend Darge taes away 3 and gives you '. Hou dro < but ic u 4.#ret taes 4 and gives 6. Hou tae one from Darge and give it to #ret in e@change for 3 more.Hou give those 3 to Darge and she gives you an ale and an orange. Fran comes and taesthe ale Darge gave you and gives you a ear. Hou give the ear to #ret in e@change for anale. Fran then taes an ale from Darge$ gives it to #ret for an orange$ gives you the orangefor an ale.

ow many ears do you haveSubmitted

Answer

one

Fran gave you a ear in e@change of the ale which Darge gave you. And you gave that earto #ret in e@change for an ale. All the others e@changes involved ales and;or organges.Four coules are going to the movie. 2ach row holds eight seats. #etty and im don5t want to sitne@t to Alice and Tom. Alice and Tom don5t want to sit ne@t to Oertrude and #ill. Cn the otherhand$Sally and #ob don5t want to sit ne@t to #etty and im.

ow can the coules arrange themselves in a row so that they all sit where they would lieSubmitted by : Tara Smith


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Answer

From the given data$ it can be inferred that1Sally ? #ob" 0CT #etty ? im" 0CT Alice ? Tom" 0CT Oertrude ? #ill"

A" 0CT #" means A and # can not seat ne@t to each other.

0ow$ it is obvious that #etty ? im" and Alice ? Tom" will occuy the corner seats as both ofthem can have only one neighbour. Therefore$Oertrude ? #ill" will seat ne@t to #etty ? im"Sally ? #ob" will seat ne@t to Oertrude ? #ill"Alice ? Tom" will seat ne@t to Sally ? #ob"

Thus$ there are two ossible arrangements ! a mirror images of each other.

&. #etty ? im" ! Oertrude ? #ill" ! Sally ? #ob" ! Alice ? Tom"'. Alice ? Tom" ! Sally ? #ob" ! Oertrude ? #ill" ! #etty ? im"Substitute digits for the letters to mae the following addition roblem true. ( + E

E E

A E

% A +

'''''''''''''''''''

+ ( D +

0ote that the leftmost letter can5t be Bero in any word. Also$ there must be a one!to!one maingbetween digits and letters. e.g. if you substitute 3 for the letter $ no other letter can be 3 and allother in the uBBle must be 3.

Answer

/t is obvious that S%& and T%,.

Also$ 8 2" should be greater than &7 and hence$ 2 8 8 2" must '7. Thus$ there are 3ossible values for 2$ " air1 ($ )" or se trial!n!error and everything will fit!in.

( + E 2 8 5 1 6

E E 9 6 6 9 8

A E 4 6

% A + % 4 1

''''''''''''''''''' '''''''''''''''''''

+ ( D + 1 2 5 1

hen Socrates was imrisoned for being a disturbing influence$ he was held in high esteem byhis guards. All four of them hoed that something would occur that would facilitate his escae.Cne evening$ the guard who was on duty intentionally left the cell door oen so that Socratescould leave for distant arts.


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Socrates did not attemt to escae$ as it was his hilosohy that if you accet society5s rules$ youmust also accet it5s unishments. owever$ the oen door was considered by the authorities tobe a serious matter. /t was not clear which guard was on that evening. The four guards mae thefollowing statements in their defense1

Aaron1A" / did not leave the door oen.#" -lement was the one who did it.

#ob1A" / was not the one who was on duty that evening.#" Aaron was on duty.

-lement1A" #ob was the one on duty that evening.#" / hoed Socrates would escae.

avid1A" / did not leave the door oen.

#" / was not surrised that Socrates did not attemt to escae.

-onsidering that$ in total$ three statements are true$ and five statements are false$ which guard isguiltyAnswer

David is the guilt-.

0ote that GAll four of them hoed that something would occur that would facilitate his escaeG. /tmaes -lement5s statement # True and avid5s statement # False.

0ow consider each of them as a guilty$ one at a time.

Aaron o3 #lement David

A A A A

True

tmts

/f Aaron is guilty False False True True False True True False 4

/f #ob is guilty True False False False True True True False 4

/f -lement is guilty True True True False False True True False 6

/f avid is guilty True False True False False True False False %

Since in total$ three statements are true and five statements are false. /t is clear from the abovetable that avid is

Brain easer o 0044

Oiven any whole number tae the sum of the digits$ and the roduct of the digits$ and multilythese together to get a new whole number.

For e@amle$ starting with (


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And yet again 68


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T ; X " % ! T " ; H !!!!!equ/"

Also$ #angalore!Dysore train and Dysore!#angalore train arrive destination & hr and 4 hrsresectively after assing each other. /t means that #angalore!Dysore train travels ! T" ms in& hr at X m;hr and Dysore!#angalore train travels T ms in 4 hrs at H m;hr. ence$ ! T " % X andT % 4 * H

Substituting these values in equation /$ we get 4 * H " ; X % X ; H4 * H * H % X * X' * H % X

ence$ the seed of #angalore!Dysore train is T/-2 the seed of Dysore!#angalore train.owmuch faster is one train from other

Answer

/9 times

+et5s assume that everyone clined their mug with friend to his left only. /t means that there aretotal 4, clins. 0ow the right clin of each erson is left clin of the erson on right which isalready haened. ence$ there are only 4, clins.

Drs. atsherface had a garage sale. A custmer named Oina bought an old lam and a rug. Sheaid a total of Z6.'6 for everything. The rug cost '6 cents more than the lam.

ow much did each costSubmitted by : Kimi

Answer

The lamp cost N 2.0 and the rug cost N 2.7

A simle one.

Assume that the lam cost Z +.ence the rug must have cost Z + 8 7.'6"

Also$ total cost is Z 6.'6$ ence the equation 1+ 8 + 8 7.'6 % 6.'6' * + % 6+ % '.67

ence$ the lam cost Z '.67 and the rug cost Z '.


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e.g. 3(,1 38(8,%&)1 &8)%, which is a multile of 3 hence 3(, is divisable by 3.

9': henever a number X" is multilied with another number H" then the roduct X*H" will haveall the factors of X as well as all the factors of H in its set of factors.e.g. if X has factors of &$Q$$X" and H has factors of &$$=$H" then X*H has factors of&$Q$$$=$X$H".

+et0 % any series of digits e.g. 0%3(," % the number of digits in 0 e.g. if 0%3(, then %3"Q % is a number constructed in the following way 1 a &$ followed by !&" 7s$ followed by another&$ followed by !&" 7s$ followed by another &. e.g. if 0%3(, then %3 and Q would be &77&77&"0ote that Q will always be divisible by 3.

Also$ if we multily 0 with Q we are essentially reeating 0 for !&" times.e.g. if 0%3(, then %3$ Q%&77&77& and 0*Q%3(,3(,3(,

+et5s start with 0%&&&. /t is clear that 0 is divisible by 3. From 9&:"Also$ %3 and Q%&77&77&

0*Q%&&&&&&&&& , times"The resulting number &&&&&&&&& must be divisible by , as 0 and Q both are divisible by 3.

0ow$ let5s start with 0%&&&&&&&&&. /t is clear that 0 is divisible by ,.Also$ %, and Q%&77777777&77777777&0*Q%&&&&&&&&&... '< times"The resulting number &&&&&&&... '< times" must be divisible by '< as 0 is divisible by , and Q isdivisible by 3.

=eeat the same rocedure for 0%&&&&&&&... '< times" The resulting number &&&&&&&... )&times" must be divisible by )& as 0 is divisible by '< and Q is divisible by 3.

Similarly$ for 0%&&&&&&&... )& times" The resulting number &&&&&&&... '43 times" must bedivisible by '43 as 0 is divisible by )& and Q is divisible by 3.

Thus$ &&&&&&&... '43 times" is divisible by '43.

Thans to =yan utcherson for solution RRRedaran bought a little bo@ of midget matches$ each one inch in length. e found that he couldarrange them all in the form of a triangle whose area was Eust as many square inches as therewere matches.

e then used u si@ of the matches$ and found that with the remainder he could again constructanother triangle whose area was Eust as many square inches as there were matches.

And using another si@ matches he could again do recisely the same.

ow many matches were there in the bo@ originally

0ote that the match!bo@ can hold ma@imum of 67 matches.Answer

>nitiall-& there were /2 or %, matches in the match)3o.

There are 4' matches in the bo@ with which he could form a triangle '7$ &6$


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construct a star using two triangle. The sum of all number lying in straight lines should be same.This can be easilty understood by the fig. and hence solved.Submitted by : Vaibhav Gupta

3e have one answer where sum of all the numbers lying in straight lines is (%.

If you have others, do submit them.

Brain easer o 0055

Dontu$ #antu$ -hantu and Qintu have ets.

Dontu says$ G/f Qintu and / each have a dog$ then e@actly one of #antu and -hantu has adog.G

#antu says$ G/f -hantu and / each have a cat$ then e@actly one of Dontu and Qintu has a dog.G

-hantu says$ G/f Dontu and / each have a dog$ then e@actly one of #antu and Qintu has a cat.G

Qintu says$ G/f #antu and / each have a cat$ then e@actly one of #antu and / has a dog.G

Cnly one of the four is telling the truth. ho is telling the truth

Answer

antu is telling the truth.

Kor a >K)TJ" statement to 3e false& >K part has to 3e true and TJ" part has to 3e false.

Since only one statement is true and remaining three are false$ /F art of three statements aretrue ? T20 art of one statement is true. +et5s ut the given information in table. The et!namein the normal te@t reresents the /F art and the et!name in round bracets reresents theT20 art.

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Montu antu #hantu Eintu

Montu sa-s og og" og" og

antu sa-s og" -at -at og"

#hantu sa-s og -at" og -at"

Eintu sa-s -atog"

-atog"

It is clear that the I* part of the statements made by 4ontu, 8hantu and 9intu are true asthey do not contradict each other. nd the I* part of the statement made by 'antu is false.

Thus, 'antu is telling the truth.

4ontu have a :og and may or may not have a 8at.'antu have a 8at.8hantu have a :og.9intu have a :og and a 8at.

Brain easer o 00520

Somebody mared the si@ faces of a die with the numbers &$ ' and 3 ! each number twice.The die was ut on a table. Four eole ! Abu$ #abu$ -alu and abu ! sat around the table sothat each one was able to see only three sides of the die at a glance.

Abu sees the number & and two even numbers.

#abu and -alu can see three different numbers each.

abu sees number ' twice and he can5t remember the third number.

hat number is face down on the table

Answer

um3er % is face down on the ta3le.

/f Abu can see two even numbers i.e. number ' twice$ and if abu can see number ' twice$ thennumber ' must be facing u.

0ow everything else is simle. see the following diagram"


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Da!u A!u

1

2 2

1

Calu Ba!u

Thus$ the number hidden from the view is number 3 and hence the answer.Two identical ac of cards A and # are shuffled throughly. Cne card is iced from A and shuffled

with #. The to card from ac A is turned u. /f this is the ueen of earts$ what are the chancesthat the to card in # will be the ing of eartsAnswer

2 @ 270%

There are two cases to be considered.

#A" 1 ? ing of earts is drawn from Qac A and shuffled with Qac #

Qrobability of drawing ing of earts from Qac A % &;6& as ueen of earts is not to be drawn"Qrobability of having ing of earts on the to of the Qac # % ';63

So total robability of case & % &;6&" * ';63" % ' ; 6& * 63"

#A" 2 ? ing of earts is not drawn from Qac A

Qrobability of not drawing ing of earts from Qac A % 67;6& as ueen of earts is not to bedrawn"Qrobability of having ing of earts on the to of the Qac # % &;63

So total robability of case ' % 67;6&" * &;63" % 67 ; 6& * 63"

0ow adding both the robability$ the required robability is% ' ; 6& * 63" 8 67 ; 6& * 63"% 6' ; 6& * 63"% 6' ; '


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be 3 and all other D in the uBBle must be 3.

Answer

A tough oneRRR

Since = 8 2 8 2 % &7 8 2$ it is clear that = 8 2 % &7 and neither = nor 2 is equal to 7 or 6. This isthe only entry oint to

solve it. 0ow use trial!n!error method.

E 3 E 2 1 4 1 9

E A 3 E 1 5 4 1

% E % 6 1

''''''''''''''''' '''''''''''''''''

A ( E 5 0 2 1There are '7 eole in your alicant ool$ including 6 airs of identical twins.

/f you hire 6 eole randomly$ what are the chances you will hire at least & air of identical twins0eedless to say$ this could cause trouble K""SubmAnswer

The pro3a3ilit- to hire people with at least 1 pair of identical twins is 2.28


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ence$ the robability to hire 6 eole with at least a single air of indentical twins% 3,'7;&6674% '46;,(,% 7.'6')% '6.')NittedMeeru says to ay$ G-an you figure out how many 2ggs / have in my bucetG e gives 3 clues toay1 /f the number of 2ggs / have

&. is a multile of 6$ it is a number between & and &,'. is not a multile of )$ it is a number between '7 and ',3. is not a multile of &7$ it is a number between 37 and 3,

ow many 2ggs does Meeru have in his bucet

Answer

%2 eggs

+et5s aly all 3 condition searately and ut all ossible numbers together.

First condition says that if multile of 6$ then the number is between & and &,. ence$ theossible numbers are 6$ &7$ &6$ '&$ ''$ '3$ '4$ '6$ '($ '


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Similarly$ Dr. hite must be wearing either blac suit or grey suit. #ut Dr. Orey is wearing a blacsuit. ence$ Dr. hite must be wearing a grey suit.

And$ Dr. #lac must be wearing white suit.Substitute numbers for the letters so that the following mathematical e@ressions are correct. ABC DEI G

''' = E ''' = E ''' = E

6 9

0ote that the same number must be used for the same letter whenever it aears.Answer

A42& 41& #49& D4/& "4%& K48& 4,& J4& >47

+et5s start with O/ % , * /2. 0ote that / aears on both the side. Also$ after multilying /2 by ,the answer should have / at the unit5s lace. The ossible values of /2 are &,$ ')$ 3


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From 3"$ A is -5s only son i.e. A is Dale.#ut is A5s brother which means that A is not -5s only son. ence$ our assumtion was wrong.

Thus$ - is 5s sister i.e. - is Female. And # must be -5s only son.

0ow it is clear that ? # are Dales and - is Female. A must be a Dale as only one of them is ofoosite se@ from each of the other three. And he is - ? 5s brother.ow are they related to eachother

r. o+ittle always goes waling to the clinic and taes the same time while going and whilecoming bac. Cne day he noticed something.

hen he left the home$ the hour hand and the minute hand were e@actly oosite to each otherand when he reached the clinic$ they were together.

Similarly$ when he left the clinic$ the hour hand and the minute hand were together and when hereached the home$ they were e@actly oosite to each other.

ow much time does r. o+ittle tae to reach home from the clinic Oive the minimal ossible

answer.Answer

%2 minutes /%., seconds

/n twelve hours$ the minute hand and the hour hand are together for && times. /t means that afterevery &';&& hours$ both the hands are together.

Similarly in twelve hours$ the minute hand and the hour hand are e@actly oosite to each otherfor && times. /t means that after every &';&& hours$ both the hands are oosite.

0ow$ let5s tae an e@amle. e now that at &' both the hands are together and at ( both thehands are e@actly oosite to each other.

After ($ both the hands are in oosition at 9(8&';&&": hours$ 9(8'*&';&&": hours$ 9(83*&';&&":hours and so on. The si@th such time is 9(8(*&';&&": hours which is the first time after &'. Thusafter &'$ both the hands are oosite to each other at &'13'143.(

ence$ r. o+ittle taes 3' minutes and 43.( seconds to reach home from the clinic.

Slow=un 2@ress runs between #angalore and Dumbai$ For the u as well as the down Eourney$the train leaves the starting station at &7177 QD everyday and reaches the destination at &&137QD after three days.

Dr. aani once travelled by Slow=un 2@ress from Dumbai to #angalore. ow many Slow=un

2@ress did he cross during his EourneyAnswer

Mr. Jaani crossed 7 lowun "presses during his !ourne-.

+et5s say that Dr. aani travelled by Slow=un 2@ress on ednesday &7177QD from Dumbai.The first train he would have crossed is the one scheduled to arrive at Dumbai at &&137 QD thesame day i.e. the one that left #angalore at &7177 QD on last Sunday.

Also$ he would have crossed the last train Eust before reaching #angalore on Saturday.


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Thus$ Dr. aani must have crossed < Slow=un 2@resses during his Eourney.Si@ cabins numbered &!( consecutively$ are arranged in a row and are searated by thin dividers.These cabins must be assigned to si@ staff members based on following facts.

&. Diss Shalaa5s wor requires her to sea on the hone frequently throughout the day.

'. Diss Shudha refers cabin number 6 as 6 is her lucy number.3. Dr. Shaan and Dr. Sharma often tal to each other during their wor and refers to haveadEacent cabins.

4. Dr. Sinha$ Dr. Shaan and Dr. Solani all smoe. Diss Shudha is allergic to smoe andmust have non!smoers adEacent to her.

6. Dr. Solani needs silence during wor.

-an you tell the cabin numbers of each of themAnswer

The ca3ins from left to right :1),; are of Mr. olan*i& Mr. inha& Mr. haan& Mr. harma& Misshudha and Miss hala*a.

From '"$ cabin number 6 is assigned to Diss Shudha.

As Diss Shudha is allergic to smoe and Dr. Sinha$ Dr. Shaan ? Dr. Solani all smoe$ they mustbe in cabin numbers &$ ' and 3 not necessarily in the same order. Also$ Diss Shalaa and Dr.Sharma must be in cabin 4 and (.

From 3"$ Dr. Shaan must be in cabin 3 and Dr. Sharma must be in cabin 4. Thus$ Diss Shalaais in cabin (.

As Dr. Solani needs silence during wor and Dr. Shaan is in cabin 3 who often tals to Dr.Sharma during wor$ Dr. Solani must be in cabin &. ence$ Dr. Sinha is in cabin '.

Thus$ the cabins numbers are&V Dr. Solani$'V Dr. Sinha$3V Dr. Shaan$4V Dr. Sharma$6V Diss Shudha$(V Diss ShalaaSyFi city is served by ( subway lines ! A$ 2$ /$ C$ > and I.

hen it snows$ morning service on line 2 is delayed.

hen it rains or snows$ service on the lines A$ > and I is delayed both morning andafternoon.

hen the temerature dros below '7 -$ afternoon service is cancelled on either line Aor line C$ but not both.

hen the temerature rises above 47 -$ afternoon service is cancelled on either line / orline I$ but not both.

hen service on line A is delayed or cancelled$ service on line / is also delayed.

hen service on line I is delayed or cancelled$ service on line 2 is also delayed.

Cn February &7$ it snows all day with the temerature at &)-. Cn how many lines service will bedelayed or cancelled$ including both morning and afternoonSyFi city is served by ( subway lines ! A$ 2$ /$ C$ > and I.


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hen it snows$ morning service on line 2 is delayed.

hen it rains or snows$ service on the lines A$ > and I is delayed both morning andafternoon.

hen the temerature dros below '7 -$ afternoon service is cancelled on either line Aor line C$ but not both.

hen the temerature rises above 47 -$ afternoon service is cancelled on either line / or

line I$ but not both. hen service on line A is delayed or cancelled$ service on line / is also delayed.

hen service on line I is delayed or cancelled$ service on line 2 is also delayed.

Cn February &7$ it snows all day with the temerature at &)-. Cn how many lines service will bedelayed or cancelled$ including both morning and afternoon/n a certain game$ if ' wi@somes are worth 3 changs$ and 4 changs are worth & lut$ then ( lutesare worth how many wi@somes

Answer

/t is given that' wi@somes % 3 changs

) wi@somes % &' changs !!!!! /"

Also$ given that4 changs % & lut&' changs % 3 lutes) wi@somes % 3 lutes !!!!! From /"

Therefore$( lutes % &( wi@somes

/n a certain year$ the number of girls who graduated from -ity igh School was twice the numberof boys. /f 3;4 of the girls and 6;( of the boys went to college immediately after graduation$ whatfraction of the graduates that year went to college immediately after graduation

Answer

Assume that number of boys graduated from -ity igh School % #Therefore$ number of girls graduated from -ity igh School % '*#

/t is given that 3;4 of the girls and 6;( of the boys went to college immediately after graduation.ence$ total students went to college% 3;4"'*#" 8 6;("#"% # * 3;' 8 6;("%


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ow many sacs were each of them carrying Oive the minimal ossible answer.SubmittAnswer

The mule was carr-ing sac*s and the don*e- was carr-ing 7 sac*s.

+et5s assume that the mule was carrying D sacs and the doney was carrying sacs.

As the doney told the mule$ G/f you gave me one of your sacs /5d have double what you have.G 8 & % ' * D!&" 8 & % 'D ! ' % 'D ! 3

The doney also said$ G/f / give you one of my sacs we5d have an even amount.G ! & % D 8 & % D 8 '

-omaring both the equations$'D ! 3 % D 8 'D % 6

Substituting D%6 in any of above equation$ we get % a =egistered +etter [ Send an /tem Qarcel Qost

3 -arlos Qimentelli [ Cvernight Qacage[ Send Airmail to Tibet

4 onna ToriseBa [ #uy Stams[ Send an /nsured Qacage

6 Dary nutson [ #uy a Doney Crder [ Send #oos fourth -lass

( Anthony =endler [ -omlain About a Dail -arrier [ Qic > a Qacage

Brain easer o 00164

Substitute digits for the letters to mae the following relation true. ( D

% A D E

'''''''''''''

C E E 0ote that the leftmost letter can5t be Bero in any word. Also$ there must be a one!to!onemaing between digits and letters. e.g. if you substitute 3 for the letter $ no other letter canbe 3 and all other in the uBBle must be 3.

Answer

A tough one.

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/t is obvious that -%&. Also$ the ma@imum ossible value of 2 is


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Brain easer o 00261

The letters Q$ $ =$ S$ T$ > and M$ not necessarily in that order reresents seven consecutiveintegers from '' to 33.

> is as much less than as = is greater than S.

M is greater than >. is the middle term.

Q is 3 greater than S.

-an you find the sequence of letters from the lowest value to the highest value

Answer

The seuence of letters from the lowest value to the highest value is T=HE.

From 3"$ is the middle term.

\\\ \\\ \\\ \\ \\\ \\\ \\\

From 4"$ there must be e@actly ' numbers between Q and S which gives two ossible ositions.

9&: \\\ \S\ \\\ \\ \Q\ \\\ \\\

9': \\\ \\\ \S\ \\ \\\ \Q\ \\\

From &"$ the number of letters between > and must be same as the number of letters betweenS and =. Also$ the number of letters between them can be &$ ' or 3.

>sing trial and error$ it can be found that there must be ' letters between them. Also$ it is ossible

only in otion 9': above.

9': \\\ \>\ \S\ \\ \=\ \Q\ \\\

From '" M must be the highest and the remaining T must be the lowest number.

\T\ \>\ \S\ \\ \=\ \Q\ \M\

Thus$ the sequence of letters from the lowest value to the highest value is T>S=QM.A contractor had emloyed &77 labourers for a flyover construction tas. e did not allow anywoman to wor without her husband. Also$ atleast half the men woring came with their wives.

e aid five ruees er day to each man$ four rues to each woman and one ruee to each

child. e gave out '77 ruees every evening.

ow many men$ women and children were woring with the constructorAnswer

1, men& 12 women and 72 children were wor*ing with the constructor.

+et5s assume that there were X men$ H women and I children woring with the constructor.ence$


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X 8 H 8 I % &776X 8 4H 8 I % '77

2liminating X and H in turn from these equations$ we getX % 3I ! '77H % 377 ! 4I

As if woman wors$ her husband also wors and atleast half the men woring came with theirwivesK the value of H lies between X and X;'. Substituting these limiting values in equations$ weget

if H % X$377 ! 4I % 3I ! '77


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The pilgrim had 7 flowers& initiall- and he offered 8 flowers to each od.

Assume that the ilgrim had X flowers initially and he offered H flowers to each Ood.

From the above figure$ there are )X !


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ow long would it tae for him to cut 4) ieces e can not fold the stri and also$ can not stactwo or more stris and cut them together.SubmiAnswer

/7 seconds.

To get 4) ieces$ the boy have to ut only 4< cuts. i.e. he can cut 4( ieces in 4( seconds. Aftergetting 4( ieces$ he will have a ' inches long iece. e can cut it into two with Eust a one cut in &second. ence$ total of 4< seconds.tted by : Kimi

The cricet match between /ndia and Qaistan was over.

arbhaEan scored more runs than Oanguly.

Sachin scored more runs than +a@man but less than ravid

#adani scored as much runs as Agarar but less than ravid and more than Sachin.

Oanguly scored more runs than either Agarar or ravid.

2ach batsman scored &7 runs more than his immediate batsman. The lowest score was &7 runs.ow much did each one of them score

Answer

A simle one. >se the given facts and ut down all the layers in order. The order is as followwith arbhaEan$ the highest scorer and +a@man$ the lowest scorer.

&. arbhaEan'. Oanguly3. ravid4. #adani$ Agarar6. Sachin(. +a@man

Also$ as the lowest score was &7 runs. +a@man must have scored &7$ Sachin '7$ #adani ?Agarar 37 and so on.

&. arbhaEan ! (7 runs'. Oanguly ! 67 runs3. ravid ! 47 runs4. #adani$ Agarar ! 37 runs each6. Sachin ! '7 runs(. +a@man ! &7 runs

There are &7 statements written on a iece of aer1

&. At least one of statements , and &7 is true.

'. This either is the first true or the first false statement.3. There are three consecutive statements$ which are false.4. The difference between the numbers of the last true and the first true statement divides

the number$ that is to be found.6. The sum of the numbers of the true statements is the number$ that is to be found.(. This is not the last true statement.


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&7. There are no three consecutive true statements.

Find the minimal ossible numberSubmitted

Answer

The nume3r is /20.

/f statement ( is false$ it creates a arado@. ence$ tatement , must 3e true.

-onsider Statement '1

/f it is true$ it must be the f irst true statement. Ctherwise$ it creates a arado@.

/f it is false$ it must be the second false statement. Ctherwise$ it creates a arado@.

/n both the cases$ tatement 1 is false.

As Statement & is false$ tatement 9 and tatement 10 3oth are falsei.e. there are threeconsecutive true statements.

& ' 3 4 6 ( < ) , &7

False ! ! ! ! True ! ! False False

+et^5s assume that Statement 3 is false i.e. there are no three consecutive false statements. /tmeans that Statement ' and Statement ) must be true$ else there will be three consecutive falsestatements.

& ' 3 4 6 ( < ) , &7

False True False ! ! True ! True False False

Also$ atleast two of Statements 4$ 6 and < must be true as there are three consecutive truestatements.

According to Statement )$ the number that is to be found is the ercentage of true statements.ence$ number is either 67 or (7. 0ow if Statement < is true$ then the number of each truestatement divides the number$ that is to be found. #ut < and ) do not divide either 67 or (7.ence$ Statement < is false which means that Statement 4 and 6 are true. #ut Statement 6contradicts the Statement ). ence$ our assumtion that Statement 3 is false is wrong andtatement % is truei.e. there are 3 consecutive false statements which means that tatement 8is falseas there is no other ossibilities of 3 consecutive false statements.

Also$ tatement 7 is trueas Statement ( is not the last true statement.

& ' 3 4 6 ( < ) , &7

False ! True ! ! True True False False False

According to Statement


89/144

& ' 3 4 6 ( < ) , &7

False True True True False True True False False False

0ow$ the conditions for the number to be found are1

&. The numebr is divisible by 6 Statement 4"'. The numebr is divisible by '$ 3$ 4$ ($ < Statement


90/144

Thus$ at the end Anit and TeEas$ both have the same number of ales.

Cn evey Sunday Amar$ Abar and Anthony lunch together at Qreetam!a!haba where theyorder lassi based on following facts.

&. >nless neither Amar nor Abar have lassi$ Anthony must have it.'. /f Amar does not have lassi$ either Abar or Anthony or both have it.3. Anthony has lassi only if either Amar or Abar or both have it.4. Abar and Anthony never have lassi together.

ho orders" lassiAnswer

Amar and Anthon- 3oth have lassi whereas A*3ar never does.

*act "($ can be alternatively stated that ;either mar or kbar or nthony must havelassi;.

*rom *act "!$, it can be infered that either mar or kbar must have lassi.

1ow, from *act "&$, it is apparent that nthony too must have lassi. 'ut according to *act"#$, kbar cannot have lassi when nthony does.

Brain easer o 00191

eciher this sentence.

B L I M K M L B M

L C E D / B G M M M E

/ B G L + M / B G K M / M

B ) ) / B G K D B I .

Answer

Start with I#O and I#O. /t should be either Gthe;thenG or Gyou;yourG combination as they aearmore.


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B L I M K M L B M

o ! s t a l e s a r e t ; o s e

L C E D / B G M M M E

t ; i n g s : o u s e e ; e n

/ B G L + M / B G K M / M

: o u t a H e : o u r e : e s

B ) ) / B G K D B I .

o : o u r g o a l s.

Brain easer o 00001

At what time immediately rior to Si@ C5cloc the hands of the cloc are e@actly oosite toeach other. Oive the e@act time in hours$ minutes and seconds.

Answer

/t is obvious that between 6 C5cloc and ( C5cloc the hands will not be e@actly oosite to eachother. /t is also obvious that the hands will be oosite to each other Eust before 6 C5cloc. 0ow tofind e@act time1

The hour hand moves & degree for every &' degrees that the minute hand moves. +et the hourhand be X degree away from 6 C5cloc. Therefore the minute hand is &'X degree away from &'C5cloc.

Therefore solving for X

Angle between minute hand and &' C5cloc 8 Angle between &' C5cloc and 4 C5cloc 8 Anglebetween 4 C5cloc and hour hand % &)7&'X 8 &'7 8 37!X" % &)7&&X % 37ence X % 37;&& degreeshour hand is X degree away from 6 C5cloc"

0ow each degree the hour hand moves is ' minutes.

Therefore minutes are% ' * 37;&&% (7;&&% 6.46 means 6 minutes '


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Ali #aba had four sons$ to whom he bequeathed his 3, camels$ with the roviso that the legacybe divided in the following way 1

The oldest son was to receive one half the roerty$ the ne@t a quarter$ the third an eighth and theyoungest one tenth. The four brothers were at a loss as how to divide the inheritance amongthemselves without cutting u a camel$ until a stranger aeared uon the scene.ismounting from his camel$ he ased if he might hel$ for he new Eust what to do. The brothersgratefully acceted his offer.

Adding his own camel to Ali #aba5s 3,$ he divided the 47 as er the will. The oldest son received'7$ the ne@t &7$ the third 6 and the youngest 4. Cne camel remained 1 this was his$ which hemounted and rode away.

Scratching their heads in amaBement$ they started calculating. The oldest thought 1 is not '7greater than the half of 3, Someone must have received less than his roer share R #ut eachbrother discovered that he had received more than his due. ow is it ossibleAnswer

They too their ercentages from 47 and not from 3,$ so they got more than their share.

The oldest son got &;' of 47 % '7 which is 7.6 moreThe second son got &;4 of 47 % &7 which is 7.'6 moreThe third son got &;) of 47 % 6 which is 7.&'6 moreThe youngest son got &;&7 of 47 % 4 which is 7.& more

And the stranger got &;47 of 47 % & which is 7.7'6 more As he is not suosed to get anything"

All these fractions add to % 7.6 8 7.'6 8 7.&'6 8 7.& 8 7.7'6 % & which stranger too away.There is a family arty consisting of two fathers$ two mothers$ two sons$ one father!in!law$ onemother!in!law$ one daughter!in!law$ one grandfather$ one grandmother and one grandson.

hat is the minimum number of ersons required so that this is ossible

Answer

There are total ' coules and a son. Orandfather and Orand mother$ their son and his wife andagain their son. So total 6 eole.

Orandfather$ OrandmotherPP

Son$ wifePP

Son

A man went into a fast food restaurant and ate a meal costing =s. &76$ giving the accountant a=s. 677 note. e et the change$ came bac a few minutes later and had some food aced forhis girl friend. e gave the accountant a =s. &77 note and received =s. '7 in change. +ater theban told the accountant that both the =s. 677 and the =s. &77 notes were counterfeit.

ow much money did the restaurant lose /gnore the rofit of the food restaurant.Answer


93/144

Je lost s.,00

First time restaurant has given food worth =s.&76 and =s. 3,6 change. Similarly second time$food worth =s.)7 and =s.'7 change. ere$ we are not considering food restaurant rofits.

+ D E

' D E A

'''''''''

6 5 1

2ach of seven digits from 7!, are reresented by a different letter above such that the subtractionis true.

hat word reresents 3(6&Answer

%,1 represents B".

+et5s assign ossible values to each letter and then use trial!n!error.

S must be &.

Then under +" must be greater than 6. /f is ($ then + is 7. #ut then A must be 7 or & which isimossible. ence$ the ossible values of are


94/144

#lar* is the landlord.

ssume each statement true, one at a time and see that no other statement is contradicted.

in. Thus, =dmund is not the landlord either.


95/144

BNs s@ouse KNs si!ling FNs sister'in'la

"ale# "ale# "eale#

''''''''''''''''''''''''''''''''''''''''''''''''''''''

Case K F B

Case F B K

8ase II is not possible as ' ? 9 are married to each other and both are male. -ence, @ isthe married man.

Brain easer o 00041

A olygon has &3'6 diagonals. ow many vertices does it have

Answer

The formula to find number of diagonals " given total number of vertices or sides 0" is

* " ' #

D = '''''''''''

2

>sing the formula$ we get&3'6 * ' % 0 * 0 ! 3"0'! 30 ! '(67 % 7

Solving the quadratic equation$ we get 0 % 63 or !67

/t is obvious that answer is %as number of vertices can not be negative.

lternatively, you can derive the formula as triange has 0 diagonals, quadrangel has (,pentagon has 5, he)agon has 2 and so on......

-ence the series is 0, 0, 0, (, 5, 2, , ........ "as diagram with &,( or ! vertices will have 0diagonals$.

Asing the series one can arrive to the formula given above.

Brain easer o 0006

A cube is made of a white material$ but the e@terior is ainted blac.

/f the cube is cut into &'6 smaller cubes of e@actly the same siBe$ how many of the cubes willhave atleast ' of their sides ainted blac

Answer

//


96/144

!% of the cubes have =B8T>le tipped you off tothis.

Brain easer o 0028

/magine a triangle of coins on a table so that the first row has one coin in it and the secondrow has two coins in it and so on. /f you can only move one coin at a time$ how many movesdoes it tae to mae the triangle oint the other way

For a triangle with two row it is one$ for a triangle with three rows it is two$ for a triangle withfour rows it is three.

For a traingle with five rows is it fourSubmitted

Answer

/t taes 6 moves to mae the triangle with 6 rows oint the other way.

7 % a coin that has not been moved.X % the old osition of the moved coin) % the new osition of the moved coin.

\\\\\\\\X\\\\\\\

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