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.
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Can you explain how this card trick works?
Delight your friends with this cunning trick! Can you explain how
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?
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
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.
Crosses can be drawn on number grids of various sizes. What do you
notice when you add opposite ends?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
Replace each letter with a digit to make this addition correct.
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?
What are the missing numbers in the pyramids?
Three dice are placed in a row. Find a way to turn each one so that
the three numbers on top of the dice total the same as the three
numbers on the front of the dice. Can you find all the ways to. . . .
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.
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?
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
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. . . .
This article suggests some ways of making sense of calculations involving positive and negative numbers.
Start with four numbers at the corners of a square and put the
total of two corners in the middle of that side. Keep going... Can
you estimate what the size of the last four numbers will be?
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Use your logical reasoning to work out how many cows and how many
sheep there are in each field.
Find out about Magic Squares in this article written for students. Why are they magic?!
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
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.
Find the sum of all three-digit numbers each of whose digits is
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
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
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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
This is an adding game for two players.
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?
Here is a chance to play a version of the classic Countdown Game.
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!
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
The Scot, John Napier, invented these strips about 400 years ago to
help calculate multiplication and division. Can you work out how to
use Napier's bones to find the answer to these multiplications?
Where can you draw a line on a clock face so that the numbers on
both sides have the same total?
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?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?