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?
Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten
numbers from the bags above so that their total is 37.
Can you explain how this card trick works?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Delight your friends with this cunning trick! Can you explain how
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This challenge extends the Plants investigation so now four or more children are involved.
Here is a chance to play a version of the classic Countdown Game.
Find out about Magic Squares in this article written for students. Why are they magic?!
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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?
Arrange the numbers 1 to 16 into a 4 by 4 array. Choose a number.
Cross out the numbers on the same row and column. Repeat this
process. Add up you four numbers. Why do they always add up to 34?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Special clue numbers related to the difference between numbers in
two adjacent cells and values of the stars in the "constellation"
make this a doubly interesting problem.
Replace each letter with a digit to make this addition correct.
Can you be the first to complete a row of three?
This Sudoku, based on differences. Using the one clue number can you find the solution?
What are the missing numbers in the pyramids?
A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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
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.
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?
This article suggests some ways of making sense of calculations involving positive and negative numbers.
There are nasty versions of this dice game but we'll start with the nice ones...
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Choose any three by three square of dates on a calendar page.
Circle any number on the top row, put a line through the other
numbers that are in the same row and column as your circled number.
Repeat. . . .
Whenever two chameleons of different colours meet they change
colour to the third colour. Describe the shortest sequence of
meetings in which all the chameleons change to green if you start
with 12. . . .
Here is a chance to play a fractions version of the classic
If you wrote all the possible four digit numbers made by using each
of the digits 2, 4, 5, 7 once, what would they add up to?
How can we help students make sense of addition and subtraction of negative numbers?
Find a great variety of ways of asking questions which make 8.
This article explains how to make your own magic square to mark a special occasion with the special date of your choice on the top line.
This challenge is to make up YOUR OWN alphanumeric. Each letter
represents a digit and where the same letter appears more than once
it must represent the same digit each time.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
The country Sixtania prints postage stamps with only three values 6 lucres, 10 lucres and 15 lucres (where the currency is in lucres).Which values cannot be made up with combinations of these postage. . . .
Use these four dominoes to make a square that has the same number of dots on each side.
What is the sum of all the digits in all the integers from one to
An account of some magic squares and their properties and and how to construct them for yourself.
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. . . .