10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
What is the best way to shunt these carriages so that each train
can continue its journey?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
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?
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
An activity making various patterns with 2 x 1 rectangular tiles.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
These practical challenges are all about making a 'tray' and covering it with paper.
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 find all the different ways of lining up these Cuisenaire
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
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?
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
How many different triangles can you make on a circular pegboard that has nine pegs?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This activity investigates how you might make squares and pentominoes from Polydron.
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.
How many triangles can you make on the 3 by 3 pegboard?
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.