This problem is designed to help children to learn, and to use, the two and three times tables.
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?
Use your logical reasoning to work out how many cows and how many sheep there are in each field.
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.
Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?
Amy has a box containing domino pieces but she does not think it is a complete set. She has 24 dominoes in her box and there are 125 spots on them altogether. Which of her domino pieces are missing?
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?
Can you score 100 by throwing rings on this board? Is there more than way to do it?
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.
If the numbers 5, 7 and 4 go into this function machine, what numbers will come out?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
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.
Use 4 four times with simple operations so that you get the answer 12. Can you make 15, 16 and 17 too?
The value of the circle changes in each of the following problems. Can you discover its value in each problem?
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?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
56 406 is the product of two consecutive numbers. What are these two numbers?
Number problems at primary level that require careful consideration.
Number problems at primary level that may require determination.
The triangles in these sets are similar - can you work out the lengths of the sides which have question marks?
This number has 903 digits. What is the sum of all 903 digits?
Here is a picnic that Petros and Michael are going to share equally. Can you tell us what each of them will have?
A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.
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?
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?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
What is happening at each box in these machines?
There are four equal weights on one side of the scale and an apple on the other side. What can you say that is true about the apple and the weights from the picture?
Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.
This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.
Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.
Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.
Find a great variety of ways of asking questions which make 8.
Where can you draw a line on a clock face so that the numbers on both sides have the same total?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
Use the information to work out how many gifts there are in each pile.
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?
Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?
Chandrika was practising a long distance run. Can you work out how long the race was from the information?
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 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.
This task combines spatial awareness with addition and multiplication.
The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?
I'm thinking of a number. When my number is divided by 5 the remainder is 4. When my number is divided by 3 the remainder is 2. Can you find my number?
After training hard, these two children have improved their results. Can you work out the length or height of their first jumps?
What is the sum of all the three digit whole numbers?
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?
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?
In November, Liz was interviewed for an article on a parents' website about learning times tables. Read the article here.