A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

The clues for this Sudoku are the product of the numbers in adjacent squares.

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

The Zargoes use almost the same alphabet as English. What does this birthday message say?

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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.

Given the products of adjacent cells, can you complete this Sudoku?

A few extra challenges set by some young NRICH members.

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 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?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you find all the ways to get 15 at the top of this triangle of numbers?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

In this matching game, you have to decide how long different events take.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?