Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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?
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" .
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.
There are ten children in Becky's group. Can you find a set of numbers for each of them? Are there any other sets?
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...
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
Can you find what the last two digits of the number $4^{1999}$ are?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
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 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?
Follow the clues to find the mystery number.
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?
This article for teachers describes how number arrays can be a useful reprentation 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?
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.
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.
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
What is the lowest number which always leaves a remainder of 1 when divided by each of the numbers from 2 to 10?
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?
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?
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?
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?
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
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?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Can you order the digits from 1-6 to make a number which is divisible by 6 so when the last digit is removed it becomes a 5-figure number divisible by 5, and so on?
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?
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. Can you find all the numbers in each set from these clues?
Can you find a way to identify times tables after they have been shifted up?
A game that tests your understanding of remainders.
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?