A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
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?
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?
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?
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?
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
Can you make a 3x3 cube with these shapes made from small cubes?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
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?
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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
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.
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 coach your rowing eight to win?
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
Use these four dominoes to make a square that has the same number of dots on each side.
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
The graph represents a salesman’s area of activity with the
shops that the salesman must visit each day. What route around the
shops has the minimum total distance?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you beat the computer in the challenging strategy game?
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
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?
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.
Can you use the information to find out which cards I have used?
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 of balls?
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?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Three teams have each played two matches. The table gives the total
number points and goals scored for and against each team. Fill in
the table and find the scores in the three matches.
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?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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?
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.
Use the 'double-3 down' dominoes to make a square so that each side has eight dots.
56 406 is the product of two consecutive numbers. What are these
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of
three children. Use the information to find out what the three
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
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.