Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Can you put the 25 coloured tiles into the 5 x 5 square so that no
column, no row and no diagonal line have tiles of the same colour
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.
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Using different numbers of sticks, how many different triangles are
you able to make? Can you make any rules about the numbers of
sticks that make the most triangles?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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!
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
The ancient Egyptians were said to make right-angled triangles
using a rope with twelve equal sections divided by knots. What
other triangles could you make if you had a rope like this?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal 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?
How many triangles can you make on the 3 by 3 pegboard?
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?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
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.
Take a rectangle of paper and fold it in half, and half again, to
make four smaller rectangles. How many different ways can you fold
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
This problem is based on a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
10 space travellers are waiting to board their spaceships. There
are two rows of seats in the waiting room. Using the rules, where
are they all sitting? Can you find all the possible ways?
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.
Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.
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!
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
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?
Take 5 cubes of one colour and 2 of another colour. How many
different ways can you join them if the 5 must touch the table and
the 2 must not touch the table?
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
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
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?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
In how many ways can you stack these rods, following the rules?
What could the half time scores have been in these Olympic hockey
How many models can you find which obey these rules?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?