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?
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?
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.
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?
Can you make a 3x3 cube with these shapes made from small cubes?
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.
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
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?
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
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?
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
Find out why these matrices are magic. Can you work out how they were made? Can you make your own Magic Matrix?
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?
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?
Can you see how these factor-multiple chains work? Find the chain
which contains the smallest possible numbers. How about the largest
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
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?
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.
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?
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
Exploring balance and centres of mass can be great fun. The
resulting structures can seem impossible. Here are some images to
encourage you to experiment with non-breakable objects of your own.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
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.
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
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
Can you coach your rowing eight to win?
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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
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.
Find at least one way to put in some operation signs (+ - x ÷)
to make these digits come to 100.
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?
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?
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Using only six straight cuts, find a way to make as many pieces of
pizza as possible. (The pieces can be different sizes and shapes).
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over 2 coins, then one third show heads. How many coins are there altogether?
In 1871 a mathematician called Augustus De Morgan died. De Morgan
made a puzzling statement about his age. Can you discover which
year De Morgan was born in?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.