Does this 'trick' for calculating multiples of 11 always work? Why or why not?

Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.

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

Choose any four consecutive even numbers. Multiply the two middle numbers together. Multiply the first and last numbers. Now subtract your second answer from the first. Try it with your own. . . .

Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?

Mathematicians are always looking for efficient methods for solving problems. How efficient can you be?

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?

Visitors to Earth from the distant planet of Zub-Zorna were amazed when they found out that when the digits in this multiplication were reversed, the answer was the same! Find a way to explain. . . .

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

These pictures and answers leave the viewer with the problem "What is the Question". Can you give the question and how the answer follows?

This number has 903 digits. What is the sum of all 903 digits?

56 406 is the product of two consecutive numbers. What are these two numbers?

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

Play this game and see if you can figure out the computer's chosen number.

The value of the circle changes in each of the following problems. Can you discover its value in each problem?

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

Number problems at primary level that may require resilience.

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

Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.

Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?

If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

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?

Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .

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

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

If you had any number of ordinary dice, what are the possible ways of making their totals 6? What would the product of the dice be each time?

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!

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

Find the number which has 8 divisors, such that the product of the divisors is 331776.

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?

Find the next number in this pattern: 3, 7, 19, 55 ...

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Which set of numbers that add to 10 have the largest product?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

Alf describes how the Gattegno chart helped a class of 7-9 year olds gain an awareness of place value and of the inverse relationship between multiplication and division.

There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?

Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

This jar used to hold perfumed oil. It contained enough oil to fill granid silver bottles. Each bottle held enough to fill ozvik golden goblets and each goblet held enough to fill vaswik crystal. . . .

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

Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?

What is the smallest number of answers you need to reveal in order to work out the missing headers?