When newspaper pages get separated at home we have to try to sort
them out and get things in the correct order. How many ways can we
arrange these pages so that the numbering may be different?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
The challenge here is to find as many routes as you can for a fence
to go so that this town is divided up into two halves, each with 8
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.?
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.
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
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
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
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
Place the 16 different combinations of cup/saucer in this 4 by 4
arrangement so that no row or column contains more than one cup or
saucer of the same colour.
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?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Let's say you can only use two different lengths - 2 units and 4
units. Using just these 2 lengths as the edges how many different
cuboids can you make?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Can you draw a square in which the perimeter is numerically equal
to the area?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Stuart's watch loses two minutes every hour. Adam's watch gains one
minute every hour. Use the information to work out what time (the
real time) they arrived at the airport.
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
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!
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
Can you cover the camel with these pieces?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Find your way through the grid starting at 2 and following these
operations. What number do you end on?
How many different ways can you find to join three equilateral
triangles together? Can you convince us that you have found them
What happens when you try and fit the triomino pieces into these
This activity investigates how you might make squares and pentominoes from Polydron.
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?
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?
How many different rhythms can you make by putting two drums on the
In this town, houses are built with one room for each person. There
are some families of seven people living in the town. In how many
different ways can they build their houses?
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?
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?
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!
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
In the planet system of Octa the planets are arranged in the shape
of an octahedron. How many different routes could be taken to get
from Planet A to Planet Zargon?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
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?
What could the half time scores have been in these Olympic hockey
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?
How many models can you find which obey these rules?
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
Investigate all the different squares you can make on this 5 by 5
grid by making your starting side go from the bottom left hand
point. Can you find out the areas of all these squares?
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.
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?