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

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

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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?

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?

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

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

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

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?

There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?

What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?

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?

Can you replace the letters with numbers? Is there only one solution in each case?

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?

Six friends sat around a circular table. Can you work out from the information who sat where and what their profession were?

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

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

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

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.

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?

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

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?

Find out about Magic Squares in this article written for students. Why are they magic?!

Can you work out some different ways to balance this equation?

What happens when you round these three-digit numbers to the nearest 100?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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

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

Have a go at balancing this equation. Can you find different ways of doing it?

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

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

This task follows on from Build it Up and takes the ideas into three dimensions!

Use the numbers and symbols to make this number sentence correct. How many different ways can you find?

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?

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

Number problems at primary level that require careful consideration.

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

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

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

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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