Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Can you shunt the trucks so that the Cattle truck and the Sheep
truck change places and the Engine is back on the main line?
What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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.
If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?
Use the clues to colour each square.
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
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
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?
This problem focuses on Dienes' Logiblocs. What is the same and
what is different about these pairs of shapes? Can you describe the
shapes in the picture?
Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
How many trains can you make which are the same length as Matt's,
using rods that are identical?
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?
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Cut four triangles from a square as shown in the picture. How many
different shapes can you make by fitting the four triangles back
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
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
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
How many different rhythms can you make by putting two drums on 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.
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?
If you have three circular objects, you could arrange them so that
they are separate, touching, overlapping or inside each other. Can
you investigate all the different possibilities?
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?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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!
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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 10 in the circles so that each number is the
difference between the two numbers just below it.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
My coat has three buttons. How many ways can you find to do up all
A dog is looking for a good place to bury his bone. Can you work
out where he started and ended in each case? What possible routes
could he have taken?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue.
She wants to fit them together to make a cube so that each colour shows on each face just once.
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?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.