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?

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

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?

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

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

When the number x 1 x x x is multiplied by 417 this gives the answer 9 x x x 0 5 7. Find the missing digits, each of which is represented by an "x" .

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

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. . . .

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?

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

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?

Becky created a number plumber which multiplies by 5 and subtracts 4. What do you notice about the numbers that it produces? Can you explain your findings?

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

Three people chose this as a favourite problem. It is the sort of problem that needs thinking time - but once the connection is made it gives access to many similar ideas.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?

Explore the relationship between simple linear functions and their graphs.

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?

Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?

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. . . .

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?

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.

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

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?

A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?

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

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?

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

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

"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 ...?

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

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

Factor track is not a race but a game of skill. The idea is to go round the track in as few moves as possible, keeping to the rules.

Follow this recipe for sieving numbers and see what interesting patterns emerge.

Have a go at balancing this equation. Can you find different ways of doing it?

Can you work out some different ways to balance this equation?

Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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?

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.

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

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...

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

Number problems at primary level that may require determination.

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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

Number problems at primary level to work on with others.