In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?
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.
Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?
This task follows on from Build it Up and takes the ideas into three dimensions!
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.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?
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?
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 make square numbers by adding two prime numbers together?
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?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).
Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.
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!
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?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
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?
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.
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!
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
Using the statements, can you work out how many of each type of rabbit there are in these pens?
How would you count the number of fingers in these pictures?
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?
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Investigate the different distances of these car journeys and find out how long they take.
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
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.
A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
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.
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?
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?
Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.
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?
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?
You have 5 darts and your target score is 44. How many different ways could you score 44?
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?
Find the sum of all three-digit numbers each of whose digits is odd.
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?
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?
What is the sum of all the three digit whole numbers?
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?
If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?