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

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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

Can you make square numbers by adding two prime numbers together?

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

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?

This article for primary teachers suggests ways in which to help children become better at working systematically.

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?

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

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

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

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

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

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?

You have 5 darts and your target score is 44. How many different ways could you score 44?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

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

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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?

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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?

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

Given the products of adjacent cells, can you complete this Sudoku?

There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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

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

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

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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.

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

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.?

Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?

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.

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

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

Can you substitute numbers for the letters in these sums?

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