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1. Three people A,B,C are each given 2 colours, for a total of 6

colors ( blue, green, orange, purple, red & yellow ). In

comparing the colours they received, B makes the following

observation " the number of common letters between the two colours

is one less than the number of A's common letters & one more

than the no. of C's common letters." Find the colours each person

received . ( Can there be more than one answer ?)

2. A pirate ship captures a treasure of 1000 golden coins. The

treasure has to be split among 5 pirates on the ship. These

pirates are a bit too much concious of their status. the booty

will be shared in order of their rank 1,2,3,4 & 5. The pirates

have the following 3 characteristics : infinitely Smart,

Bloodthirsty & Greedy.

Starting with pirate 5 they can make a proposal on how to split

their treasure . This proposal can either be accepted or else

the pirate will be thrown overboard. A proposal is accepted IF &

ONLY IF a majority of the pirates agree on it. What proposal

should the pirate 5 make ?

(Please note that throwing overboard would materialise if & only if

there is a majority decision. A person would support a proposal only

if he thinks :

a) this will get him his biggest gain.

b) there is no better way out.

A pirate is infinitely:

* smart => he will consider all cases possible.

* bloodthirsty => he will kill other pirates if possible.

* greedy => he won't agree to a seemingly O.K. type negotiated

proposal if he thinks that he has a better chance

elsewhere. ( i.e. on some other case of proposal he

thinks will come along...). He will concede to a

proposal only if that is his biggest gain possible

under the cicumstances...)

One thing that arises from the order of seniority mentioned is

that, given two people , the one with the higher rank can kill the

other if he wants. So pirate 2 will never want a case where only he &

pirate 1 remain. So he won't want to throw pirate 3 overboard, for ,

then 1 can kill 2 & get all. So if in a condition where 4 & 5 have

already been thrown overboard after their proposals have been

rejected, if 3 proposes to give one coin to 2 & keep the remaining

999 to himself, 2 doesn't have a choice but to agree. 1 will

definitely oppose this, for if 3 is thrown overboard , he can kill 2

& get all the coins.

But 2 would like to get more coins than just one & so he would want

to keep 4 on board for, it might increase his chances of getting more

from the proposal that 4 makes. 1 & 3 would definitely want to throw

4 overboard for, that maximises their chances of getting more

coins.... Like wise, reason & get down to 5.....)