Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2
litres. Find a way to pour 9 litres of drink from one jug to
another until you are left with exactly 3 litres in three of the
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
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?
How many trapeziums, of various sizes, are hidden in this picture?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Can you use this information to work out Charlie's house number?
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?
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
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
On a digital 24 hour clock, at certain times, all the digits are
consecutive. How many times like this are there between midnight
and 7 a.m.?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
In this matching game, you have to decide how long different events take.
Investigate the different ways you could split up these rooms so
that you have double the number.
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
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?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
What could the half time scores have been in these Olympic hockey
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
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.
In how many ways can you stack these rods, following the rules?
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!
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake