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?
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?
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
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.
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 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?
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.
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?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Can you use the information to find out which cards I have used?
Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's
there is one digit, between the two 2's there are two digits, and
between the two 3's there are three digits.
Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.
Can you beat the computer in the challenging strategy game?
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Use these four dominoes to make a square that has the same number of dots on each side.
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Can you coach your rowing eight to win?
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?
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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?
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.
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?
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
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?
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.
Use the numbers in the box below to make the base of a top-heavy
pyramid whose top number is 200.
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.
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
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
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.
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
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.
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?
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?
Can you make a 3x3 cube with these shapes made from small cubes?
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 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
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
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
The clockmaker's wife cut up his birthday cake to look like a clock
face. Can you work out who received each piece?
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?