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?

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

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

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?

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?

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?

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

The clues for this Sudoku are the product of the numbers in adjacent squares.

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?

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

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

Play this game and see if you can figure out the computer's chosen number.

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

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

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?

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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.

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

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

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?

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!?

Think of any three-digit number. Repeat the digits. The 6-digit number that you end up with is divisible by 91. Is this a coincidence?

Guess the Dominoes for child and adult. Work out which domino your partner has chosen by asking good questions.

Find the number which has 8 divisors, such that the product of the divisors is 331776.

What is the smallest number of answers you need to reveal in order to work out the missing headers?

I'm thinking of a number. My number is both a multiple of 5 and a multiple of 6. What could my number be?

Using the digits 1 to 9, the number 4396 can be written as the product of two numbers. Can you find the factors?

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

Nine squares are fitted together to form a rectangle. Can you find its dimensions?

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

Can you work out what size grid you need to read our secret message?

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

This task depends on learners sharing reasoning, listening to opinions, reflecting and pulling ideas together.

Look at three 'next door neighbours' amongst the counting numbers. Add them together. 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.

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?

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

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

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?

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

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.

Explore the relationship between simple linear functions and their graphs.

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?

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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 that may require resilience.