Combinatorics

problem

Stage 5 Cipher Challenge

Age

16 to 18

Challenge level

Can you crack these very difficult challenge ciphers? How might you systematise the cracking of unknown ciphers?
problem

A Fine Thing?

Age

16 to 18

Challenge level

Second challenge cipher
problem

One Basket or Group Photo

Age

7 to 18

Challenge level

Libby Jared helped to set up NRICH and this is one of her favourite problems. It's a problem suitable for a wide age range and best tackled practically.
problem

Euromaths

Age

11 to 14

Challenge level

How many ways can you write the word EUROMATHS by starting at the top left hand corner and taking the next letter by stepping one step down or one step to the right in a 5×5 array?
problem

Cube Paths

Age

11 to 14

Challenge level

Given a 2 by 2 by 2 skeletal cube with one route 'down' the cube. How many routes are there from A to B?
problem

Domino Tetrads

Age

11 to 14

Challenge level

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

Russian Cubes

Age

14 to 16

Challenge level

I want some cubes painted with three blue faces and three red faces. How many different cubes can be painted like that?
problem

Penta Colour

Age

14 to 16

Challenge level

In how many different ways can I colour the five edges of a pentagon so that no two adjacent edges are the same colour?
problem

Snowman

Age

14 to 16

Challenge level

All the words in the Snowman language consist of exactly seven letters formed from the letters {s, no, wm, an). How many words are there in the Snowman language?
problem

Olympic Magic

Age

14 to 16

Challenge level

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?