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?

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.

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.

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

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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

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

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.

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

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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.

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?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

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?

Find out about Magic Squares in this article written for students. Why are they magic?!

You need to find the values of the stars before you can apply normal Sudoku rules.

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

Four small numbers give the clue to the contents of the four surrounding cells.

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

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.

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?

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?

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

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

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

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

A few extra challenges set by some young NRICH members.

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?

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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?

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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....?

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. . . .

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

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

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

This Sudoku, based on differences. Using the one clue number can you find the solution?