During the third hour after midnight the hands on a clock point in
the same direction (so one hand is over the top of the other). At
what time, to the nearest second, does this happen?
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
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.
On a digital clock showing 24 hour time, over a whole day, how many
times does a 5 appear? Is it the same number for a 12 hour clock
over a whole day?
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.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
What could the half time scores have been in these Olympic hockey
These rectangles have been torn. How many squares did each one have
inside it before it was ripped?
This practical challenge invites you to investigate the different
squares you can make on a square geoboard or pegboard.
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
How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?
How many solutions can you find to this sum? Each of the different letters stands for a different number.
Can you order pictures of the development of a frog from frogspawn
and of a bean seed growing into a plant?
How many ways can you find of tiling the square patio, using square
tiles of different sizes?
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?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?
My cousin was 24 years old on Friday April 5th in 1974. On what day
of the week was she born?
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?
Can you put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Different combinations of the weights available allow you to make different totals. Which totals can you make?
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.
Use the numbers and symbols to make this number sentence correct. How many different ways can you find?
My local DIY shop calculates the price of its windows according to the area of glass and the length of frame used. Can you work out how they arrived at these prices?
In this matching game, you have to decide how long different events take.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
An investigation that gives you the opportunity to make and justify
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?
Place this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
What is the smallest number of tiles needed to tile this patio? Can
you investigate patios of different sizes?
In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?
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
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.?
Cut differently-sized square corners from a square piece of paper
to make boxes without lids. Do they all have the same volume?
Can you draw a square in which the perimeter is numerically equal
to the area?
The pages of my calendar have got mixed up. Can you sort them out?
There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.
Do you notice anything about the solutions when you add and/or
subtract consecutive negative numbers?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
This activity investigates how you might make squares and pentominoes from Polydron.
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 different triangles can you make on a circular pegboard
that has nine pegs?
How can you put five cereal packets together to make different
shapes if you must put them face-to-face?