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.

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

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?

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

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?

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

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

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

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?

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?

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....?

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

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

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

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?

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

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

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

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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?

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?

What could the half time scores have been in these Olympic hockey matches?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

Try out the lottery that is played in a far-away land. What is the chance of winning?

When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?

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.

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

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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

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?

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?

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

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

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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?

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?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.