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?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

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

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

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

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

This Sudoku requires you to do some working backwards before working forwards.

A Sudoku that uses transformations as supporting clues.

Solve the equations to identify the clue numbers in this Sudoku problem.

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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

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.

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

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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?

A few extra challenges set by some young NRICH members.

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

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?

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

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

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.

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

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

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

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?

Given the products of diagonally opposite cells - can you complete this Sudoku?

This challenge involves calculating the number of candles needed on birthday cakes. It is an opportunity to explore numbers and discover new things.

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

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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

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

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

Two sudokus in one. Challenge yourself to make the necessary connections.

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

Two sudokus in one. Challenge yourself to make the necessary connections.