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.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

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 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?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

What is the best way to shunt these carriages so that each train can continue its journey?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

A few extra challenges set by some young NRICH members.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

How many solutions can you find to this sum? Each of the different letters stands for a different number.

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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

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

My dice has inky marks on each face. Can you find the route it has taken? What does each face look like?

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

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Can you use this information to work out Charlie's house number?

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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

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.

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

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

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

What is the smallest number of coins needed to make up 12 dollars and 83 cents?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?