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

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

By selecting digits for an addition grid, what targets can you make?

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?

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

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

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.

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?

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

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.

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.

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

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.

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?

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?

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?

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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?

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

Use the differences to find the solution to this Sudoku.

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.

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!

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 diagonally opposite cells - can you complete this Sudoku?

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

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

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?

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

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

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 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?"

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

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

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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

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.

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

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

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

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?

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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

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

Use the clues about the shaded areas to help solve this sudoku