Are these statements always true, sometimes true or never true?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
What happens when you add three numbers together? Will your answer be odd or even? How do you know?
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!
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?
You have 5 darts and your target score is 44. How many different
ways could you score 44?
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
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 article gives you a few ideas for understanding the Got It! game and how you might find a winning strategy.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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
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?
Find the sum of all three-digit numbers each of whose digits is
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.
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
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?
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!
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This challenge combines addition, multiplication, perseverance and even proof.
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?
Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?
This task combines spatial awareness with addition and multiplication.
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!
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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?!
Here is a chance to play a version of the classic Countdown Game.
If you have ten counters numbered 1 to 10, how many can you put into pairs that add to 10? Which ones do you have to leave out? Why?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
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?
Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
Find a great variety of ways of asking questions which make 8.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?
A game for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Claire thinks she has the most sports cards in her album. "I have
12 pages with 2 cards on each page", says Claire. Ross counts his
cards. "No! I have 3 cards on each of my pages and there are. . . .
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
If the numbers 5, 7 and 4 go into this function machine, what
numbers will come out?