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

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?

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

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

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

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

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

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

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?"

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"?

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

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the 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?

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

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

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

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.

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?

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?

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

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

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?

Given the products of diagonally opposite cells - can you complete 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.

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

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 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?

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.

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?

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

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

Using the statements, can you work out how many of each type of rabbit there are in these pens?

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.

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

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

There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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

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 are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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 problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?