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.
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
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.?
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.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
What could the half time scores have been in these Olympic hockey
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
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?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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?
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?
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.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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 the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
How many trapeziums, of various sizes, are hidden in this picture?
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?
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?
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 these three beads into bags? How many different ways can you do it? How could you record what you've done?
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!
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
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?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same