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. . . .

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?

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

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 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?

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

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

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

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?

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?

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

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?

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

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.

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

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

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

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

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

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.

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

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?

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?

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

A Sudoku that uses transformations as supporting clues.

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

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

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?

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

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

A few extra challenges set by some young NRICH members.

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 work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

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

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?

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.

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

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?