Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
You have 4 red and 5 blue counters. How many ways can they be
placed on a 3 by 3 grid so that all the rows columns and diagonals
have an even number of red counters?
Investigate the different ways you could split up these rooms so
that you have double the number.
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.
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
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?
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
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!
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 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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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
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.
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
How many trapeziums, of various sizes, are hidden in this picture?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
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.?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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 could the half time scores have been in these Olympic hockey
These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
In how many ways can you stack these rods, following the rules?
These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.
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?
In this matching game, you have to decide how long different events take.
Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!