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

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.

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

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

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.

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?

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

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

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

A few extra challenges set by some young NRICH members.

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.

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

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".

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

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

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

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?

A Sudoku that uses transformations as supporting clues.

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

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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?

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?

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.

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?

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

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

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

How long does it take to brush your teeth? Can you find the matching length of time?

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....?

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

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

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

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

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.

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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