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.
Delight your friends with this cunning trick! Can you explain how
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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?
Crosses can be drawn on number grids of various sizes. What do you notice when you add opposite ends?
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Find out about Magic Squares in this article written for students. Why are they magic?!
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?
Replace each letter with a digit to make this addition correct.
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?
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. . . .
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.
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.
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.
Here is a chance to play a version of the classic Countdown Game.
Find the sum of all three-digit numbers each of whose digits is
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
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!
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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 see why 2 by 2 could be 5? Can you predict what 2 by 10
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.
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.
The letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
There are nasty versions of this dice game but we'll start with the nice ones...
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
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.
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
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!
Can you find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?