This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

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?

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.

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

In this matching game, you have to decide how long different events take.

This challenge extends the Plants investigation so now four or more children are involved.

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

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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?

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

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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?

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

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

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?

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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.

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.

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

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

A Sudoku that uses transformations as supporting clues.

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

Alice's mum needs to go to each child's house just once and then back home again. How many different routes are there? Use the information to find out how long each road is on the route she took.

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

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. . . .

How many trapeziums, of various sizes, are hidden in this picture?

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

On a digital 24 hour clock, at certain times, all the digits are consecutive. How many times like this are there between midnight and 7 a.m.?

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

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.

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

Try out the lottery that is played in a far-away land. What is the chance of winning?

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.

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

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

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

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

On a digital clock showing 24 hour time, over a whole day, how many times does a 5 appear? Is it the same number for a 12 hour clock over a whole day?