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?

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?

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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?

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?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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.

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.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

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

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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.

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

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

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 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.

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

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.

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 shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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

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

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

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?

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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

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

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

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?

These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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

Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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?

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

A few extra challenges set by some young NRICH members.

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

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