Combinations

problem

Clocked

Age

11 to 14

Challenge level

2 out of 3

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
problem

Domino Tetrads

Age

11 to 14

Challenge level

3 out of 3

Is it possible to use all 28 dominoes arranging them in squares of four? What patterns can you see in the solution(s)?
problem

Six Times Five

Age

11 to 14

Challenge level

3 out of 3

How many six digit numbers are there which DO NOT contain a 5?
problem

Even Up

Age

11 to 14

Challenge level

3 out of 3

Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
problem

Coins

Age

11 to 14

Challenge level

3 out of 3

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?
problem

Almost Constant Digits

Age

11 to 14

Challenge level

3 out of 3

How many 10-digit numbers containing only 1s, 2s and 3s can you write?
problem

Nine or Ten?

Age

11 to 14

Challenge level

3 out of 3

Is a score of 9 more likely than a score of 10 when you roll three dice?
problem

Trominoes

Age

11 to 16

Challenge level

2 out of 3

Can all but one square of an 8 by 8 Chessboard be covered by Trominoes?
problem

Flora the Florist

Age

14 to 16

Challenge level

1 out of 3

Flora has roses in three colours. What is the greatest number of identical bunches she can make, using all the flowers?
problem

Coin Tossing Games

Age

14 to 16

Challenge level

2 out of 3

You and I play a game involving successive throws of a fair coin. Suppose I pick HH and you pick TH. The coin is thrown repeatedly until we see either two heads in a row (I win) or a tail followed by a head (you win). What is the probability that you win?