Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
Here are the prices for 1st and 2nd class mail within the UK. You have an unlimited number of each of these stamps. Which stamps would you need to post a parcel weighing 825g?
On the table there is a pile of oranges and lemons that weighs exactly one kilogram. Using the information, can you work out how many lemons there are?
Rocco ran in a 200 m race for his class. Use the information to find out how many runners there were in the race and what Rocco's finishing position was.
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.
Annie cut this numbered cake into 3 pieces with 3 cuts so that the numbers on each piece added to the same total. Where were the cuts and what fraction of the whole cake was each piece?
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?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.
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?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
Use the information to work out how many gifts there are in each pile.
Look on the back of any modern book and you will find an ISBN code. Take this code and calculate this sum in the way shown. Can you see what the answers always have in common?
Find another number that is one short of a square number and when you double it and add 1, the result is also a square number.
On a calculator, make 15 by using only the 2 key and any of the four operations keys. How many ways can you find to do it?
There are three buckets each of which holds a maximum of 5 litres. Use the clues to work out how much liquid there is in each bucket.
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.
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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?
Investigate the different distances of these car journeys and find out how long they take.
If the answer's 2010, what could the question be?
Find the next number in this pattern: 3, 7, 19, 55 ...
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
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 task follows on from Build it Up and takes the ideas into three dimensions!
Generate large numbers then give the values of each digit.
Number problems at primary level that may require resilience.
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
What is happening at each box in these machines?
What is the sum of all the three digit whole numbers?
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
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?
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?
Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.
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?
Put a number at the top of the machine and collect a number at the bottom. What do you get? Which numbers get back to themselves?
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?
There are over sixty different ways of making 24 by adding, subtracting, multiplying and dividing all four numbers 4, 6, 6 and 8 (using each number only once). How many can you find?
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?
This number has 903 digits. What is the sum of all 903 digits?
Investigate the totals you get when adding numbers on the diagonal of this pattern in threes.
I throw three dice and get 5, 3 and 2. Add the scores on the three dice. What do you get? Now multiply the scores. What do you notice?
These alphabet bricks are painted in a special way. A is on one brick, B on two bricks, and so on. How many bricks will be painted by the time they have got to other letters of the alphabet?
In this section from a calendar, put a square box around the 1st, 2nd, 8th and 9th. Add all the pairs of numbers. What do you notice about the answers?
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 draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?