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?
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?
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?
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?
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
Design an arrangement of display boards in the school hall which fits the requirements of different people.
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?
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?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Can you cover the camel with these pieces?
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?
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?
What happens when you try and fit the triomino pieces into these
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
Use the clues to colour each square.
How many different shapes can you make by putting four right-
angled isosceles triangles together?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
In how many ways can you fit two of these yellow triangles
together? Can you predict the number of ways two blue triangles can
be fitted together?
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?
How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
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?
An activity making various patterns with 2 x 1 rectangular tiles.
Explore the different snakes that can be made using 5 cubes.
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
The Red Express Train usually has five red carriages. How many ways
can you find to add two blue carriages?
This challenge is about finding the difference between numbers which have the same tens digit.
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 focus on finding all possible solutions so working in a systematic way will ensure none are left out.
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
My coat has three buttons. How many ways can you find to do up all
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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?
How many models can you find which obey these rules?
How many different rhythms can you make by putting two drums on the
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
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!
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
A magician took a suit of thirteen cards and held them in his hand
face down. Every card he revealed had the same value as the one he
had just finished spelling. How did this work?