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.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

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

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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?

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?

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

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.

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

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

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?

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

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.

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?

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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

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....?

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

What is the smallest number of jumps needed before the white rabbits and the grey rabbits can continue along their path?

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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.

Can you create jigsaw pieces which are based on a square shape, with at least one peg and one hole?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

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. . . .

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

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

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?

The Zargoes use almost the same alphabet as English. What does this birthday message say?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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.

An investigation that gives you the opportunity to make and justify predictions.

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

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.

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

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.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?