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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Can you make the green spot travel through the tube by moving the
yellow spot? Could you draw a tube that both spots would follow?
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
If these balls are put on a line with each ball touching the one in
front and the one behind, which arrangement makes the shortest line
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.
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?
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?
Can you make a 3x3 cube with these shapes made from small cubes?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Use the information to work out how many gifts there are in each
Use the 'double-3 down' dominoes to make a square so that each side
has eight dots.
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?
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
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?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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 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?
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.
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 out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
Imagine picking up a bow and some arrows and attempting to hit the
target a few times. Can you work out the settings for the sight
that give you the best chance of gaining a high score?
Can you number the vertices, edges and faces of a tetrahedron so
that the number on each edge is the mean of the numbers on the
adjacent vertices and the mean of the numbers on the adjacent
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
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
Peter, Melanie, Amil and Jack received a total of 38 chocolate
eggs. Use the information to work out how many eggs each person
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
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?
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?
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.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Can you guess the colours of the 10 marbles in the bag? Can you
develop an effective strategy for reaching 1000 points in the least
number of rounds?
A 3 digit number is multiplied by a 2 digit number and the
calculation is written out as shown with a digit in place of each
of the *'s. Complete the whole multiplication sum.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?