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

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.

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 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.

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.

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

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?

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

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

A few extra challenges set by some young NRICH members.

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

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?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

A Sudoku that uses transformations as supporting clues.

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

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?

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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.

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

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

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

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.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

By selecting digits for an addition grid, what targets can you make?

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

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?

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

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.

How many different rectangles can you make using this set of rods?

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

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.

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?

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