Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?

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?

56 406 is the product of two consecutive numbers. What are these two numbers?

Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?

A 3 digit number is multiplied by a 2 digit number and the calculation is written out as shown with a digit in place of each of the *'s. Complete the whole multiplication sum.

Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

The number 8888...88M9999...99 is divisible by 7 and it starts with the digit 8 repeated 50 times and ends with the digit 9 repeated 50 times. What is the value of the digit M?

This problem is designed to help children to learn, and to use, the two and three times tables.

In this game, you can add, subtract, multiply or divide the numbers on the dice. Which will you do so that you get to the end of the number line first?

What is the largest number you can make using the three digits 2, 3 and 4 in any way you like, using any operations you like? You can only use each digit once.

Number problems at primary level that may require determination.

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?

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.

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?

Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.

Suppose we allow ourselves to use three numbers less than 10 and multiply them together. How many different products can you find? How do you know you've got them all?

Take the number 6 469 693 230 and divide it by the first ten prime numbers and you'll find the most beautiful, most magic of all numbers. What is it?

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?

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?

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?

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!

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?

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?

This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?

This article for teachers looks at how teachers can use problems from the NRICH site to help them teach division.

Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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?

Chandrika was practising a long distance run. Can you work out how long the race was from the information?

Use the information to work out how many gifts there are in each pile.

Where can you draw a line on a clock face so that the numbers on both sides have 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?

How would you count the number of fingers in these pictures?

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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?

Use this information to work out whether the front or back wheel of this bicycle gets more wear and tear.

Four Go game for an adult and child. Will you be the first to have four numbers in a row on the number line?

Grandma found her pie balanced on the scale with two weights and a quarter of a pie. So how heavy was each pie?

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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?

What do you notice about the date 03.06.09? Or 08.01.09? This challenge invites you to investigate some interesting dates yourself.

Each clue number in this sudoku is the product of the two numbers in adjacent cells.