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
These practical challenges are all about making a 'tray' and covering it with paper.
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?
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
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.
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?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
How many DIFFERENT quadrilaterals can be made by joining the dots
on the 8-point circle?
Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.
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 is the smallest cuboid that you can put in this box so that
you cannot fit another that's the same into it?
Swap the stars with the moons, using only knights' moves (as on a
chess board). What is the smallest number of moves possible?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
How many triangles can you make on the 3 by 3 pegboard?
Building up a simple Celtic knot. Try the interactivity or download
the cards or have a go on squared paper.
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
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.
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?
How many models can you find which obey these rules?
A thoughtful shepherd used bales of straw to protect the area
around his lambs. Explore how you can arrange the bales.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
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?
Are all the possible combinations of two shapes included in this
set of 27 cards? How do you know?
Can you find all the different ways of lining up these Cuisenaire
Number problems at primary level that require careful consideration.
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 put the numbers from 1 to 15 on the circles so that no
consecutive numbers lie anywhere along a continuous straight line?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
What is the best way to shunt these carriages so that each train
can continue its journey?
Can you help the children find the two triangles which have the
lengths of two sides numerically equal to their areas?
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
How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?
An investigation that gives you the opportunity to make and justify
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Can you replace the letters with numbers? Is there only one solution in each case?
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
A tetromino is made up of four squares joined edge to edge. Can
this tetromino, together with 15 copies of itself, be used to cover
an eight by eight chessboard?
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
An activity making various patterns with 2 x 1 rectangular tiles.
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Use two dice to generate two numbers with one decimal place. What happens when you round these numbers to the nearest whole number?
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?
Have a go at balancing this equation. Can you find different ways of doing it?