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?

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

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?

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

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

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

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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?

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

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

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

A Sudoku with clues given as sums of entries.

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

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

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

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

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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.

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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.

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?

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.

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

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

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

This challenge is about finding the difference between numbers which have the same tens digit.

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?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

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

What is the date in February 2002 where the 8 digits are palindromic if the date is written in the British way?

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?

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

Systematically explore the range of symmetric designs that can be created by shading parts of the motif below. Use normal square lattice paper to record your results.

Can you find the chosen number from the grid using the clues?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

I was in my car when I noticed a line of four cars on the lane next to me with number plates starting and ending with J, K, L and M. What order were they in?

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?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

Can you help the children find the two triangles which have the lengths of two sides numerically equal to their areas?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

What is the smallest number of coins needed to make up 12 dollars and 83 cents?