How many solutions can you find to this sum? Each of the different letters stands for a different number.

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?

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

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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?

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

This Sudoku requires you to do some working backwards before working forwards.

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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.

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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?

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 find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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?

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.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

This Sudoku, based on differences. Using the one clue number can you find the solution?

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.

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

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

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

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.

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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?"

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

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

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?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

Four small numbers give the clue to the contents of the four surrounding cells.

Use the differences to find the solution to this Sudoku.

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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. . . .

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

A pair of Sudoku puzzles that together lead to a complete solution.

You need to find the values of the stars before you can apply normal Sudoku rules.

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?