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?

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

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?

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?

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?

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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" .

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

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?

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

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

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

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

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

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?

Number problems at primary level that may require determination.

Number problems at primary level to work on with others.

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. . . .

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

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

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

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?

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

For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?

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

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

The discs for this game are kept in a flat square box with a square hole for each disc. Use the information to find out how many discs of each colour there are in the box.

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

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

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.

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?

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?

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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?

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

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

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

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

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?

Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.

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?

Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?

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?

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