The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Exactly 195 digits have been used to number the pages in a book.
How many pages does the book have?
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?
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?
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?
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
Alice and Brian are snails who live on a wall and can only travel
along the cracks. Alice wants to go to see Brian. How far is the
shortest route along the cracks? Is there more than one way to go?
Using the statements, can you work out how many of each type of
rabbit there are in these pens?
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
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?
I was in my car when I noticed a line of four cars on the lane next
to me with number plates starting and ending with J, K, L and M.
What order were they in?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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?
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 8 in the circles so that no consecutive
numbers are joined by a line.
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?
Can you substitute numbers for the letters in these sums?
Can you use this information to work out Charlie's house number?
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?
Find the product of the numbers on the routes from A to B. Which
route has the smallest product? Which the largest?
Can you work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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
Given the products of adjacent cells, can you complete this Sudoku?
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!
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.
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?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?
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 order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
This task follows on from Build it Up and takes the ideas into three dimensions!
Can you find all the ways to get 15 at the top of this triangle of numbers?
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.
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
What do you notice about the date 03.06.09? Or 08.01.09? This
challenge invites you to investigate some interesting dates
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?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Arrange eight of the numbers between 1 and 9 in the Polo Square
below so that each side adds to the same total.