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?

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

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?

Your vessel, the Starship Diophantus, has become damaged in deep space. Can you use your knowledge of times tables and some lightning reflexes to survive?

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?

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

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

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

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?

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?

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

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?

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

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.

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?

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

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?

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?

Are these statements always true, sometimes true or never true?

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

One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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?

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

Does this 'trick' for calculating multiples of 11 always work? Why or why not?

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

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

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

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

Can you find any two-digit numbers that satisfy all of these statements?

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

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

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?

Factors and Multiples game for an adult and child. How can you make sure you win this game?

Is there an efficient way to work out how many factors a large number has?

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

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

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?

Can you complete this jigsaw of the multiplication square?

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 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?

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.

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?

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

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. . . .

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

Number problems at primary level that may require resilience.