Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?

Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

The sum of the first 'n' natural numbers is a 3 digit number in which all the digits are the same. How many numbers have been summed?

What is the remainder when 2^2002 is divided by 7? What happens with different powers of 2?

Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

Benâ€™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?

How many different sets of numbers with at least four members can you find in the numbers in this box?

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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

I am thinking of three sets of numbers less than 101. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?

Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?

Katie and Will have some balloons. Will's balloon burst at exactly the same size as Katie's at the beginning of a puff. How many puffs had Will done before his balloon burst?

What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.

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

How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?

Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.

Make a set of numbers that use all the digits from 1 to 9, once and once only. Add them up. The result is divisible by 9. Add each of the digits in the new number. What is their sum? Now try some. . . .

Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?

The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?

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

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?

Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.

The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?

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?

Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?

How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?

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

Find the highest power of 11 that will divide into 1000! exactly.

Can you find any perfect numbers? Read this article to find out more...

This article for teachers describes how number arrays can be a useful reprentation for many number concepts.

Number problems at primary level that may require determination.

Number problems at primary level to work on with others.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .

Norrie sees two lights flash at the same time, then one of them flashes every 4th second, and the other flashes every 5th second. How many times do they flash together during a whole minute?

Four of these clues are needed to find the chosen number on this grid and four are true but do nothing to help in finding the number. Can you sort out the clues and find the number?

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 red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?

An investigation that gives you the opportunity to make and justify predictions.

Can you find a way to identify times tables after they have been shifted up?

Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two digit numbers are multiplied to give a four digit number, so that the expression is correct. How many different solutions can you find?

Investigate the different shaped bracelets you could make from 18 different spherical beads. How do they compare if you use 24 beads?

Can you find what the last two digits of the number $4^{1999}$ are?

Do you know a quick way to check if a number is a multiple of two? How about three, four or six?