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 ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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!
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
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?
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
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!
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Winifred Wytsh bought a box each of jelly babies, milk jelly bears,
yellow jelly bees and jelly belly beans. In how many different ways
could she make a jolly jelly feast with 32 legs?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
There are 44 people coming to a dinner party. There are 15 square
tables that seat 4 people. Find a way to seat the 44 people using
all 15 tables, with no empty places.
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.
There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and
lollypops for 7p in the sweet shop. What could each of the children
buy with their money?
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.
An investigation that gives you the opportunity to make and justify
Tim had nine cards each with a different number from 1 to 9 on it.
How could he have put them into three piles so that the total in
each pile was 15?
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.
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?
The Zargoes use almost the same alphabet as English. What does this
birthday message say?
This task depends on groups working collaboratively, discussing and reasoning to agree a final product.
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?
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?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Find all the different shapes that can be made by joining five
equilateral triangles edge to edge.
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?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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 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?
Place eight dots on this diagram, so that there are only two dots
on each straight line and only two dots on each circle.
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?
Sitting around a table are three girls and three boys. Use the
clues to work out were each person is sitting.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
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?
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.