Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
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?
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?
In this investigation, you must try to make houses using cubes. If
the base must not spill over 4 squares and you have 7 cubes which
stand for 7 rooms, what different designs can you come up with?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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.
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
How many models can you find which obey these rules?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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 help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
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.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you use this information to work out Charlie's house number?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
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?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
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?
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
George and Jim want to buy a chocolate bar. George needs 2p more
and Jim need 50p more to buy it. How much is the chocolate bar?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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.?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
How could you put eight beanbags in the hoops so that there are
four in the blue hoop, five in the red and six in the yellow? Can
you find all the ways of doing this?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
You cannot choose a selection of ice cream flavours that includes
totally what someone has already chosen. Have a go and find all the
different ways in which seven children can have ice cream.
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the different ways you could split up these rooms so
that you have double the number.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
What could the half time scores have been in these Olympic hockey
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!