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.

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?

Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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

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

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

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

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

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?

Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

A game that tests your understanding of remainders.

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.

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

Got It game for an adult and child. How can you play so that you know you will always win?

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

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

Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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?

Given the products of adjacent cells, can you complete this Sudoku?

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

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

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

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?

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

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

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

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?

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?

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

How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?

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

If you have only four weights, where could you place them in order to balance this equaliser?

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. . . .

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

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

A game for 2 or more people. Starting with 100, subratct a number from 1 to 9 from the total. You score for making an odd number, a number ending in 0 or a multiple of 6.

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

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

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?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

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?

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.

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

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest power of two that divides exactly into 100!?

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?

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