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?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
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?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
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?
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.
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!
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?
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.?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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 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?
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?
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
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.
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.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Six friends sat around a circular table. Can you work out from the
information who sat where and what their profession were?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
In how many ways can you stack these rods, following the rules?
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?
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!
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?
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?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
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!
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
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.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?