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?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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!
Number problems at primary level that require careful consideration.
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 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?
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.
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, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
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?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
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?
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
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.
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
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 this "worm" on the 100 square and find the total of the four
squares it covers. Keeping its head in the same place, what other
totals can you make?
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?
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?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Can you arrange 5 different digits (from 0 - 9) in the cross in the
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 dice train has been made using specific rules. How many different trains can you make?
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 find all the ways to get 15 at the top of this triangle of numbers?
This task follows on from Build it Up and takes the ideas into three dimensions!
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?
Cherri, Saxon, Mel and Paul are friends. They are all different
ages. Can you find out the age of each friend using the
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?
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?
We can arrange dots in a similar way to the 5 on a dice and they
usually sit quite well into a rectangular shape. How many
altogether in this 3 by 5? What happens for other sizes?
If you had any number of ordinary dice, what are the possible ways
of making their totals 6? What would the product of the dice be
Cassandra, David and Lachlan are brothers and sisters. They range
in age between 1 year and 14 years. Can you figure out their exact
ages from the clues?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
Three children are going to buy some plants for their birthdays. They will plant them within circular paths. How could they do this?
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.
These sixteen children are standing in four lines of four, one behind the other. They are each holding a card with a number on it. Can you work out 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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
A game for 2 people. Use your skills of addition, subtraction, multiplication and division to blast the asteroids.