If you had 36 cubes, what different cuboids could you make?
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?
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.
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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.
How many models can you find which obey these rules?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?
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?
Penta people, the Pentominoes, always build their houses from five
square rooms. I wonder how many different Penta homes you can
What is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
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?
These two group activities use mathematical reasoning - one is
numerical, one geometric.
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Can you draw a square in which the perimeter is numerically equal
to the area?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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 do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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?
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!
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
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.
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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 order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Ben has five coins in his pocket. How much money might he have?
Here are four cubes joined together. How many other arrangements of four cubes can you find? Can you draw them on dotty paper?
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.
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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.
Try out the lottery that is played in a far-away land. What is the
chance of winning?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
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?
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
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?
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
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.
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?