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.
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.
Can you go from A to Z right through the alphabet in the hexagonal
All the girls would like a puzzle each for Christmas and all the
boys would like a book each. Solve the riddle to find out how many
puzzles and books Santa left.
Use the information to work out how many gifts there are in each
Can you use the information to find out which cards I have used?
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?
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.
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.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the
operations x and ÷ once and only once, what is the smallest
whole number you can make?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
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.
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.
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Pat counts her sweets in different groups and both times she has
some left over. How many sweets could she have had?
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?
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.
On the table there is a pile of oranges and lemons that weighs
exactly one kilogram. Using the information, can you work out how
many lemons there are?
There are three buckets each of which holds a maximum of 5 litres.
Use the clues to work out how much liquid there is in each bucket.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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
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?
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
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?
On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Rocco ran in a 200 m race for his class. Use the information to
find out how many runners there were in the race and what Rocco's
finishing position was.
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
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?
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Arrange the shapes in a line so that you change either colour or
shape in the next piece along. Can you find several ways to start
with a blue triangle and end with a red circle?
Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?
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
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?
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.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three