Jack has nine tiles. He put them together to make a square so that two tiles of the same colour were not beside each other. Can you find another way to do it?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

Use these four dominoes to make a square that has the same number of dots on each side.

Can you find rectangles where the value of the area is the same as the value of the perimeter?

Investigate how you can work out what day of the week your birthday will be on next year, and the year after...

Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.

Rowena's approach to this problem was particularly methodical - she made sure she found all the possible solutions.

Kirsti Ashworth, an NRICH Teacher Fellow, talks about her experiences of using rich tasks.

An article that reminds us about the value and importance of communication in the mathematics classroom.

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.