In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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.
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?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Can you use this information to work out Charlie's house number?
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?
When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
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?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Six friends sat around a circular table. Can you work out from the
information who sat where and what their profession were?
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?
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
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?
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.
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
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.
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.
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
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?
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?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
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
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.
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?
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?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
In how many ways can you stack these rods, following the rules?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.