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

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

What happens when you try and fit the triomino pieces into these two grids?

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

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

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....?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

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?

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?

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

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.

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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 work out how to balance this equaliser? You can put more than one weight on a hook.

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.

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

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 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?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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.

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

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?

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

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?

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

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?

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?

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

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

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

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?

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?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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

In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?

George and Jim want to buy a chocolate bar. George needs 2p more and Jim need 50p more to buy it. How much is the chocolate bar?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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

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