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?
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
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?
Design an arrangement of display boards in the school hall which fits the requirements of different people.
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?
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?
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?
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?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
Can you work out how to balance this equaliser? You can put more
than one weight on a hook.
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.?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
How many different triangles can you draw on the dotty grid which each have one dot in the middle?
How many different ways can you find of fitting five hexagons
together? How will you know you have found all the ways?
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?
How many different triangles can you make on a circular pegboard that has nine pegs?
Can you cover the camel with these pieces?
What happens when you try and fit the triomino pieces into these
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many triangles can you make on the 3 by 3 pegboard?
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?
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?
Use the clues to colour each square.
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?
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?
How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?
Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.
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.
How many different rhythms can you make by putting two drums on the
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?
Here you see the front and back views of a dodecahedron. Each
vertex has been numbered so that the numbers around each pentagonal
face add up to 65. Can you find all the missing numbers?
Can you find all the different triangles on these peg boards, and
find their angles?
Can you find all the different ways of lining up these Cuisenaire
How many trains can you make which are the same length as Matt's, using rods that are identical?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Alice's mum needs to go to each child's house just once and then
back home again. How many different routes are there? Use the
information to find out how long each road is on the route she
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
I like to walk along the cracks of the paving stones, but not the
outside edge of the path itself. How many different routes can you
find for me to take?
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
In this matching game, you have to decide how long different events take.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Ana and Ross looked in a trunk in the attic. They found old cloaks
and gowns, hats and masks. How many possible costumes could they
Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.