Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Use the information about Sally and her brother to find out how many children there are in the Brown family.
Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.
Can you use the information to find out which cards I have used?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
There were 22 legs creeping across the web. How many flies? How many spiders?
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Can you draw a continuous line through 16 numbers on this grid so
that the total of the numbers you pass through is as high as
As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
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.
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?
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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
In this problem you have to place four by four magic squares on the
faces of a cube so that along each edge of the cube the numbers
Can you arrange fifteen dominoes so that all the touching domino
pieces add to 6 and the ends join up? Can you make all the joins
add to 7?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Sam sets up displays of cat food in his shop in triangular stacks.
If Felix buys some, then how can Sam arrange the remaining cans in
Can you find a path from a number at the top of this network to the
bottom which goes through each number from 1 to 9 once and once
Woof is a big dog. Yap is a little dog.
Emma has 16 dog biscuits to give to the two dogs.
She gave Woof 4 more biscuits than Yap.
How many biscuits did each dog get?
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 discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Find another number that is one short of a square number and when
you double it and add 1, the result is also a square number.
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.
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?
There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.