What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.
In this matching game, you have to decide how long different events take.
Can you rearrange the biscuits on the plates so that the three
biscuits on each plate are all different and there is no plate with
two biscuits the same as two biscuits on another plate?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake
Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99
How many ways can you do it?
Systematically explore the range of symmetric designs that can be
created by shading parts of the motif below. Use normal square
lattice paper to record your results.
When intergalactic Wag Worms are born they look just like a cube.
Each year they grow another cube in any direction. Find all the
shapes that five-year-old Wag Worms can be.
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way
to share the sweets between the three children so they each get the
kind they like. Is there more than one way to do it?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
You have two egg timers. One takes 4 minutes exactly to empty and
the other takes 7 minutes. What times in whole minutes can you
measure and how?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Katie had a pack of 20 cards numbered from 1 to 20. She arranged
the cards into 6 unequal piles where each pile added to the same
total. What was the total and how could this be done?
There are 78 prisoners in a square cell block of twelve cells. The
clever prison warder arranged them so there were 25 along each wall
of the prison block. How did he do it?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
Can you find which shapes you need to put into the grid to make the
totals at the end of each row and the bottom of each column?
How many trapeziums, of various sizes, are hidden in this picture?
What is the smallest number of jumps needed before the white
rabbits and the grey rabbits can continue along their path?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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?
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.?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
Zumf makes spectacles for the residents of the planet Zargon, who
have either 3 eyes or 4 eyes. How many lenses will Zumf need to
make all the different orders for 9 families?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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 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?
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?
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?
Investigate the different ways you could split up these rooms so
that you have double the number.