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. . . .

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?

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

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

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

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

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

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?

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?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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....?

How many different triangles can you make on a circular pegboard that has nine pegs?

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

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

What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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

These practical challenges are all about making a 'tray' and covering it with paper.

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

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?

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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?

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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?

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?

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

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 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?

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

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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

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.

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.

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

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!