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?
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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 work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
Can you find all the different ways of lining up these Cuisenaire
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves 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?
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?
Find out what a "fault-free" rectangle is and try to make some of
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
These practical challenges are all about making a 'tray' and covering it with paper.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
Can you use this information to work out Charlie's house number?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
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.
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Put 10 counters in a row. Find a way to arrange the counters into
five pairs, evenly spaced in a row, in just 5 moves, using the
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
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?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
An extra constraint means this Sudoku requires you to think in
diagonals as well as horizontal and vertical lines and boxes of
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
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....?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
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.
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
How many triangles can you make on the 3 by 3 pegboard?
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?
This magic square has operations written in it, to make it into a
maze. Start wherever you like, go through every cell and go out a
total of 15!
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.