What is the best way to shunt these carriages so that each train
can continue its journey?
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?
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.
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?
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
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?
Use the clues to colour each square.
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
What happens when you try and fit the triomino pieces into these
Can you cover the camel with these pieces?
An activity making various patterns with 2 x 1 rectangular tiles.
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?
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?
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?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
These practical challenges are all about making a 'tray' and covering it with paper.
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?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Ben has five coins in his pocket. How much money might he have?
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
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.
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?
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.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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 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
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!
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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!