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.
Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.
Can you substitute numbers for the letters in these sums?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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 replace the letters with numbers? Is there only one
solution in each case?
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
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.
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!
Using the cards 2, 4, 6, 8, +, - and =, what number statements can
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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.
On my calculator I divided one whole number by another whole number and got the answer 3.125 If the numbers are both under 50, what are they?
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?
A group of children are using measuring cylinders but they lose the
labels. Can you help relabel them?
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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Can you use the information to find out which cards I have used?
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
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 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?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
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?
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?
Place the numbers 1 to 6 in the circles so that each number is the
difference between the two numbers just below it.
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?
Use these head, body and leg pieces to make Robot Monsters which
are different heights.
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
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?
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?
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
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?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
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.
Can you make square numbers by adding two prime numbers together?
Find all the numbers that can be made by adding the dots on two dice.
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 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?
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?
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?
These eleven shapes each stand for a different number. Can you use the multiplication sums to work out what they are?
Have a go at balancing this equation. Can you find different ways of doing it?