Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?
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?
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
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
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?
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?
This challenge is to design different step arrangements, which must
go along a distance of 6 on the steps and must end up at 6 high.
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!
What could the half time scores have been in these Olympic hockey
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Investigate the different ways you could split up these rooms so
that you have double the number.
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!
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?
Nina must cook some pasta for 15 minutes but she only has a 7-minute sand-timer and an 11-minute sand-timer. How can she use these timers to measure exactly 15 minutes?
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
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?
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.
Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
My cube has inky marks on each face. Can you find the route it has
taken? What does each face look like?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
Can you use the information to find out which cards I have used?
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?
Imagine that the puzzle pieces of a jigsaw are roughly a
rectangular shape and all the same size. How many different puzzle
pieces could there be?
These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.
Add the sum of the squares of four numbers between 10 and 20 to the
sum of the squares of three numbers less than 6 to make the square
of another, larger, number.
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?
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?
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
My coat has three buttons. How many ways can you find to do up all
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.
In how many ways could Mrs Beeswax put ten coins into her three
puddings so that each pudding ended up with at least two coins?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
The Vikings communicated in writing by making simple scratches on
wood or stones called runes. Can you work out how their code works
using the table of the alphabet?
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.
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?
In this maze of hexagons, you start in the centre at 0. The next
hexagon must be a multiple of 2 and the next a multiple of 5. What
are the possible paths you could take?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.