Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
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 is the sum of all the three digit whole numbers?
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!
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?
Peter, Melanie, Amil and Jack received a total of 38 chocolate eggs. Use the information to work out how many eggs each person had.
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?
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.
56 406 is the product of two consecutive numbers. What are these two numbers?
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.
Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?
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.
Use the information to work out how many gifts there are in each pile.
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?
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.
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
Can you work out what a ziffle is on the planet Zargon?
Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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?
Find the product of the numbers on the routes from A to B. Which route has the smallest product? Which the largest?
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 challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?
This task combines spatial awareness with addition and multiplication.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.
This challenge combines addition, multiplication, perseverance and even proof.
On my calculator I divided one whole number by another whole number and got the answer 3.125. If the numbers are both under 50, what are they?
Look at what happens when you take a number, square it and subtract your answer. What kind of number do you get? Can you prove it?
Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?
Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?
How would you count the number of fingers in these pictures?
This number has 903 digits. What is the sum of all 903 digits?
What is happening at each box in these machines?
If the answer's 2010, what could the question be?
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?
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?
Here is a chance to play a version of the classic Countdown Game.
Find the next number in this pattern: 3, 7, 19, 55 ...
Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Go through the maze, collecting and losing your money as you go. Which route gives you the highest return? And the lowest?
What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Number problems at primary level that may require resilience.