Combinatorics

problem
Semicircle

Age

16 to 18

Challenge level

Fourth challenge cipher
problem
Up a semitone?

Age

16 to 18

Challenge level

Fifth challenge cipher
problem
Ip?

Age

16 to 18

Challenge level

Seventh challenge cipher
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
Jluuis or even Asutguus?

Age

16 to 18

Challenge level

Sixth challenge cipher
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
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
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?