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?
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!
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?
Choose a symbol to put into the number sentence.
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
If you have only four weights, where could you place them in order
to balance this equaliser?
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...
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?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
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.
Some Games That May Be Nice or Nasty for an adult and child. Use your knowledge of place value to beat your oponent.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
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?
A game for 2 or more players with a pack of cards. Practise your
skills of addition, subtraction, multiplication and division to hit
the target score.
Can you each work out the number on your card? What do you notice?
How could you sort the cards?
This article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
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?
Find the sum of all three-digit numbers each of whose digits is
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?
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 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?
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
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?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Here is a chance to play a version of the classic Countdown Game.
A game for 2 players. Practises subtraction or other maths
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.
Delight your friends with this cunning trick! Can you explain how
Can you substitute numbers for the letters in these sums?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
This is an adding game for two players.
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Can you be the first to complete a row of three?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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?
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.