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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
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 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 a code using two different prime numbers
less than 10. You'll need to multiply them together and shift the
alphabet forwards by the result. Can you decipher the code?
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 3 rods of integer lengths, none longer than 10 units and not
using any rod more than once, you can measure all the lengths in
whole units from 1 to 10 units. How many ways can you do this?
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?
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?
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!
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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.
Fill in the numbers to make the sum of each row, column and
diagonal equal to 34. For an extra challenge try the huge American
Flag magic square.
Try adding together the dates of all the days in one week. Now
multiply the first date by 7 and add 21. Can you explain what
Fill in the missing numbers so that adding each pair of corner
numbers gives you the number between them (in the box).
You have 5 darts and your target score is 44. How many different
ways could you score 44?
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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
This dice train has been made using specific rules. How many different trains can you make?
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.
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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!
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?
This is an adding game for two players.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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?
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Place the digits 1 to 9 into the circles so that each side of the
triangle adds to the same total.
Suppose there is a train with 24 carriages which are going to be
put together to make up some new trains. Can you find all the ways
that this can be done?
Can you arrange 5 different digits (from 0 - 9) in the cross in the
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
Ram divided 15 pennies among four small bags. He could then pay any sum of money from 1p to 15p without opening any bag. How many pennies did Ram put in each bag?
What is happening at each box in these machines?
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?
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?
There are over sixty different ways of making 24 by adding,
subtracting, multiplying and dividing all four numbers 4, 6, 6 and
8 (using each number only once). How many can you find?
Annie cut this numbered cake into 3 pieces with 3 cuts so that the
numbers on each piece added to the same total. Where were the cuts
and what fraction of the whole cake was each piece?
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.