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There are a number of coins on a table. One quarter of the coins show heads. If I turn over 2 coins, then one third show heads. How many coins are there altogether?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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. . . .
56 406 is the product of two consecutive numbers. What are these two numbers?
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'.
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?
48 is called an abundant number because it is less than the sum of its factors (without itself). Can you find some more abundant numbers?
Can you make square numbers by adding two prime numbers together?
Can you work out what a ziffle is on the planet Zargon?
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
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?
Ben’s class were making 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 domino games fair? Can you explain why or why not?
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?
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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
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.
A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?
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?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
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?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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.
Can you find what the last two digits of the number $4^{1999}$ are?
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?
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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!?
Follow the clues to find the mystery number.
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
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!
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? 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?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
If you have only four weights, where could you place them in order to balance this equaliser?
How can you use just one weighing to find out which box contains the lighter ten coins out of the ten boxes?
A game that tests your understanding of remainders.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.