Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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.
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.
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
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?
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?
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.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
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?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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
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.
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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!
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
In how many ways can you stack these rods, following the rules?
What could the half time scores have been in these Olympic hockey matches?
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
These practical challenges are all about making a 'tray' and covering it with paper.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
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 we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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?