Can you locate the lost giraffe? Input coordinates to help you
search and find the giraffe in the fewest guesses.
Can you find a reliable strategy for choosing coordinates that will locate the robber in the minimum number of guesses?
If you have only four weights, where could you place them in order
to balance this equaliser?
7 balls are shaken in a container. You win if the two blue balls
touch. What is the probability of winning?
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?
Try entering different sets of numbers in the number pyramids. How does the total at the top change?
Triangle numbers can be represented by a triangular array of squares. What do you notice about the sum of identical triangle numbers?
It's easy to work out the areas of most squares that we meet, but
what if they were tilted?
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 beat the computer in the challenging strategy game?
What are the areas of these triangles? What do you notice? Can you generalise to other "families" of triangles?
Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?
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?
Can you coach your rowing eight to win?
Can you find a relationship between the number of dots on the
circle and the number of steps that will ensure that all points are
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10
We can show that (x + 1)² = x² + 2x + 1 by considering
the area of an (x + 1) by (x + 1) square. Show in a similar way
that (x + 2)² = x² + 4x + 4
How have the numbers been placed in this Carroll diagram? Which
labels would you put on each row and column?
A tilted square is a square with no horizontal sides. Can you
devise a general instruction for the construction of a square when
you are given just one of its sides?
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Help the bee to build a stack of blocks far enough to save his
friend trapped in the tower.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
Carry out some time trials and gather some data to help you decide
on the best training regime for your rowing crew.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Six balls of various colours are randomly shaken into a trianglular
arrangement. What is the probability of having at least one red in
Euler discussed whether or not it was possible to stroll around Koenigsberg crossing each of its seven bridges exactly once. Experiment with different numbers of islands and bridges.
Choose a symbol to put into the number sentence.
Can you fit the tangram pieces into the outline of this telephone?
A red square and a blue square overlap so that the corner of the red square rests on the centre of the blue square. Show that, whatever the orientation of the red square, it covers a quarter of the. . . .
Show how this pentagonal tile can be used to tile the plane and
describe the transformations which map this pentagon to its images
in the tiling.
An interactive game to be played on your own or with friends.
Imagine you are having a party. Each person takes it in turns to
stand behind the chair where they will get the most chocolate.
Can you fit the tangram pieces into the outline of Little Fung at the table?
Can you fit the tangram pieces into the outlines of these clocks?
Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?
Can you fit the tangram pieces into the outlines of the chairs?
Can you fit the tangram pieces into the outlines of these people?
Can you fit the tangram pieces into the outline of the child walking home from school?
Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?
The aim of the game is to slide the green square from the top right
hand corner to the bottom left hand corner in the least number of
A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.
An interactive activity for one to experiment with a tricky tessellation