Can you explain how this card trick works?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
In the following sum the letters A, B, C, D, E and F stand for six distinct digits. Find all the ways of replacing the letters with digits so that the arithmetic is correct.
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?
Find the sum of all three-digit numbers each of whose digits is odd.
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?
Here is a chance to play a version of the classic Countdown Game.
Ann thought of 5 numbers and told Bob all the sums that could be made by adding the numbers in pairs. The list of sums is 6, 7, 8, 8, 9, 9, 10,10, 11, 12. Help Bob to find out which numbers Ann was. . . .
Can you design a new shape for the twenty-eight squares and arrange the numbers in a logical way? What patterns do you notice?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
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.
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!
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?
We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
This is an adding game for two players.
Replace each letter with a digit to make this addition correct.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Choose any three by three square of dates on a calendar page...
Can you explain the strategy for winning this game with any target?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Delight your friends with this cunning trick! Can you explain how it works?
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.
This challenge extends the Plants investigation so now four or more children are involved.