In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
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.
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?
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?
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?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
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?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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.
Investigate the different ways you could split up these rooms so
that you have double the number.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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.
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.?
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?
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
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?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
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.
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?
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?
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.
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!
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
Can you find the chosen number from the grid using the clues?
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?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
What could the half time scores have been in these Olympic hockey
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
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 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 if you work in a systematic way, you won't leave any out.
What is the smallest number of coins needed to make up 12 dollars and 83 cents?
What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?