Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
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?
Can you find the chosen number from the grid using the clues?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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?
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
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?
Can you order the digits from 1-6 to make a number which is
divisible by 6 so when the last digit is removed it becomes a
5-figure number divisible by 5, and so on?
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Can you replace the letters with numbers? Is there only one
solution in each case?
If you put three beads onto a tens/ones abacus you could make the
numbers 3, 30, 12 or 21. What numbers can be made with six beads?
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?
Using all ten cards from 0 to 9, rearrange them to make five prime
numbers. Can you find any other ways of doing it?
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?
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
My briefcase has a three-number combination lock, but I have
forgotten the combination. I remember that there's a 3, a 5 and an
8. How many possible combinations are there to try?
There are seven pots of plants in a greenhouse. They have lost
their labels. Perhaps you can help re-label them.
If we had 16 light bars which digital numbers could we make? How
will you know you've found them all?
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
How many rectangles can you find in this shape? Which ones are
differently sized and which are 'similar'?
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?
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.
El Crico the cricket has to cross a square patio to get home. He
can jump the length of one tile, two tiles and three tiles. Can you
find a path that would get El Crico home in three jumps?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Tim's class collected data about all their pets. Can you put the
animal names under each column in the block graph using the
Ben and his mum are planting garlic. Use the interactivity to help
you find out how many cloves of garlic they might have had.
Chandra, Jane, Terry and Harry ordered their lunches from the
sandwich shop. Use the information below to find out who ordered
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
These are the faces of Will, Lil, Bill, Phil and Jill. Use the
clues to work out which name goes with each face.
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
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?
Place eight queens on an chessboard (an 8 by 8 grid) so that none
can capture any of the others.
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
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
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?
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.
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.
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!
Investigate the different ways you could split up these rooms so
that you have double the number.
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?
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?
When you throw two regular, six-faced dice you have more chance of getting one particular result than any other. What result would that be? Why is this?
What is the date in February 2002 where the 8 digits are
palindromic if the date is written in the British way?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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!
A merchant brings four bars of gold to a jeweller. How can the
jeweller use the scales just twice to identify the lighter, fake