In how many ways can you stack these rods, following the rules?
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?
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!
Six friends sat around a circular table. Can you work out from the
information who sat where and what their profession were?
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?
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.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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 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?
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?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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.
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?
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
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 Zargoes use almost the same alphabet as English. What does this
birthday message say?
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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
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.?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
How many trapeziums, of various sizes, are hidden in this picture?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
Can you use this information to work out Charlie's house number?
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?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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.
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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!
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!