Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
What happens when you try and fit the triomino pieces into these
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Make your own double-sided magic square. But can you complete both
sides once you've made the pieces?
Can you cover the camel with these pieces?
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?
How many trains can you make which are the same length as Matt's, using rods that are identical?
Use the clues to colour each square.
How many different rhythms can you make by putting two drums on the
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?
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.
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.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
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 best way to shunt these carriages so that each train
can continue its journey?
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.
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?
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?
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.
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
An activity making various patterns with 2 x 1 rectangular tiles.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below 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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?
This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.
First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.
Design an arrangement of display boards in the school hall which fits the requirements of different people.
These practical challenges are all about making a 'tray' and covering it with paper.
In this matching game, you have to decide how long different events take.