This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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?
This task follows on from Build it Up and takes the ideas into three dimensions!
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 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.
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
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?
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 jugs.
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?
Using the statements, can you work out how many of each type of rabbit there are in these pens?
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?
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.
I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?
Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.
Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.
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!
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.
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
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?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
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 each time?
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?
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!
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .
This dice train has been made using specific rules. How many different trains can you make?
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?
Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
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?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
Well now, what would happen if we lost all the nines in our number system? Have a go at writing the numbers out in this way and have a look at the multiplications table.
Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?
Can you substitute numbers for the letters in these sums?
What is happening at each box in these machines?