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

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?

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

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?

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?

What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A

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

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?

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.

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?

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?"

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?

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

Does a graph of the triangular numbers cross a graph of the six times table? If so, where? Will a graph of the square numbers cross the times table too?

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

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?

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

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?

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

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?

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

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.

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.

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

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?

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

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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...

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

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

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

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

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

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.

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

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?

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. They are the red set, the green set and the blue set. Can you find all the numbers in the sets from these clues?

Number problems at primary level that may require resilience.

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.

Can you work out how many lengths I swim each day?

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

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

Can you find different ways of creating paths using these paving slabs?

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