Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
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?
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
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?
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
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
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 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!
An activity making various patterns with 2 x 1 rectangular tiles.
Use the clues to colour each square.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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!
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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?
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.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
These practical challenges are all about making a 'tray' and covering it with paper.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
What happens when you try and fit the triomino pieces into these
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you cover the camel with these pieces?
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
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
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?
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?
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?
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
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.
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Two children made up a game as they walked along the garden paths.
Can you find out their scores? Can you find some paths of your own?