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?
Can you put the numbers 1 to 8 into the circles so that the four
calculations are correct?
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Place the numbers 1 to 10 in the circles so that each number is the
difference between the two numbers just below it.
An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.
Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
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?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?
Your challenge is to find the longest way through the network
following this rule. You can start and finish anywhere, and with
any shape, as long as you follow the correct order.
Use the interactivity to find all the different right-angled
triangles you can make by just moving one corner of the starting
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
Ben has five coins in his pocket. How much money might he have?
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?
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
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.
Mr McGregor has a magic potting shed. Overnight, the number of
plants in it doubles. He'd like to put the same number of plants in
each of three gardens, planting one garden each day. Can he do it?
Try out the lottery that is played in a far-away land. What is the
chance of winning?
What can you say about these shapes? This problem challenges you to
create shapes with different areas and perimeters.
Tom and Ben visited Numberland. Use the maps to work out the number
of points each of their routes scores.
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.
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?
Can you find all the different ways of lining up these Cuisenaire
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
Find out what a "fault-free" rectangle is and try to make some of
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.
Can you substitute numbers for the letters in these sums?
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 the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Hover your mouse over the counters to see which ones will be
removed. Click to remover them. The winner is the last one to
remove a counter. How you can make sure you win?
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?
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?
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?
Look carefully at the numbers. What do you notice? Can you make
another square using the numbers 1 to 16, that displays the same
Is it possible to place 2 counters on the 3 by 3 grid so that there
is an even number of counters in every row and every column? How
about if you have 3 counters or 4 counters or....?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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 5 darts and your target score is 44. How many different
ways could you score 44?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
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?
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
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