Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
Choose a symbol to put into the number sentence.
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
Can you make a cycle of pairs that add to make a square number
using all the numbers in the box below, once and once only?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Delight your friends with this cunning trick! Can you explain how
Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Here is a chance to play a version of the classic Countdown Game.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Start by putting one million (1 000 000) into the display of your
calculator. Can you reduce this to 7 using just the 7 key and add,
subtract, multiply, divide and equals as many times as you like?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are 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?
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.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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 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
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?
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?
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.
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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 is an adding game for two players.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
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.
Can you find all the ways to get 15 at the top of this triangle of numbers?
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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!
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?
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?
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.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you explain how this card trick works?