If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
Start with three pairs of socks. Now mix them up so that no
mismatched pair is the same as another mismatched pair. Is there
more than one way to do it?
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.
In Sam and Jill's garden there are two sorts of ladybirds with 7 spots or 4 spots. What numbers of total spots can you make?
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?
A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.
Use the information to describe these marbles. What colours must be
on marbles that sparkle when rolling but are dark inside?
Can you find out in which order the children are standing in this
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
In a square in which the houses are evenly spaced, numbers 3 and 10
are opposite each other. What is the smallest and what is the
largest possible number of houses in the square?
Find all the numbers that can be made by adding the dots on two dice.
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
There are to be 6 homes built on a new development site. They could
be semi-detached, detached or terraced houses. How many different
combinations of these can you find?
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
My coat has three buttons. How many ways can you find to do up all
Lorenzie was packing his bag for a school trip. He packed four
shirts and three pairs of pants. "I will be able to have a
different outfit each day", he said. How many days will Lorenzie be
Can you replace the letters with numbers? Is there only one
solution in each case?
Place the numbers 1 to 8 in the circles so that no consecutive
numbers are joined by a line.
Moira is late for school. What is the shortest route she can take from the school gates to the entrance?
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?
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?
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?
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?
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.
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 put the numbers 1 to 8 into the circles so that the four
calculations are correct?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Move from the START to the FINISH by moving across or down to the
next square. Can you find a route to make these totals?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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!
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
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?
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?
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?
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?