A level Maths challenges

If abcde is a 5 digit number and

3 x 1abcde = abcde1,

what is the 5 digit number abcde?

How many different ways can

it be done?

Can you make 24 with three equal numbers?

What’s the angle between the hands of

a clock at

twenty past four?

Can you make money from this game?

Pay £5 Roll the dice. If you get 5 or 6, I’ll give you £20. If you lose you can pay another £5

to try for a 6. If you roll a 6 on this, I’ll give you £35! How can you lose? Maximum 2

rolls per turn.

Alice and Bob could clear the garden in 10 hours.

Carol and Bob could clear the garden in 12 hours.

Alice and Carol could clear the garden in 15 hours.

How long will it take all three working together to clear the garden?

What is the smallest integer, n, so that

2n is a perfect square and

3n is a perfect cube?

Donald can go up stairs one step or two steps at a time, but no more.

How many different ways

can he climb a flight of 13 stairs?

A standard analogue clock falls and breaks into 3 pieces.

If the sum of the numbers on each piece is the same,

which numbers are on each piece?

Large chickens cost twice as much as small chickens.

Fred buys 5 large and 3 small chickens.

If he’d bought 3 large and 5 small, he would have saved £20.

How much does one large chicken cost?

How much does a small chicken cost?

A cat eats 5 kg of food a month.

A dog eats 6 kg.

If a collection of cats and dogs eat 56 kg of food in a month, how many

cats and how many dogs are

there?

Yvonne writes down a 5 digit number.Xavier copies the number, but puts a 1 in front to

make a 6 digit number.

Zoe copies Yvonne’s number, but puts a 1 at the end, to

make another 6 digit number.If Zoe’s number is 3 times

Xavier’s, what was Yvonne’s number?

Of 3 tiles, x, y and z, one is red, one is white and one is blue. Which is which if only 1 of the following statements is true?

• x is red• y is not red• z is not blue

If ab represents 10a + b, what is the smallest

value of efg ifab x cd = efg

The sum of 18 consecutive numbers is a square

number.What is the smallest value the square number can be?

What is the only number that can be written as thesum of two cube numbers

in two different ways?