Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
The Scot, John Napier, invented these strips about 400 years ago to help calculate multiplication and division. Can you work out how to use Napier's bones to find the answer to these multiplications?
Find out what a Deca Tree is and then work out how many leaves there will be after the woodcutter has cut off a trunk, a branch, a twig and a leaf.
What do the digits in the number fifteen add up to? How many other numbers have digits with the same total but no zeros?
Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?
Can you replace the letters with numbers? Is there only one solution in each case?
Find the sum of all three-digit numbers each of whose digits is odd.
In the multiplication sum, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
Can you substitute numbers for the letters in these sums?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
A church hymn book contains 700 hymns. The numbers of the hymns are displayed by combining special small single-digit boards. What is the minimum number of small boards that is needed?
In this 100 square, look at the green square which contains the numbers 2, 3, 12 and 13. What is the sum of the numbers that are diagonally opposite each other? What do you notice?
Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
This is a game in which your counters move in a spiral round the snail's shell. It is about understanding tens and units.
You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?
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?
This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?
Exploring the structure of a number square: how quickly can you put the number tiles in the right place on the grid?
Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?
What is the sum of all the digits in all the integers from one to one million?
Follow the clues to find the mystery number.
The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
There are six numbers written in five different scripts. Can you sort out which is which?
Each child in Class 3 took four numbers out of the bag. Who had made the highest even number?
There are nasty versions of this dice game but we'll start with the nice ones...
Find the values of the nine letters in the sum: FOOT + BALL = GAME
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" .
Amazing as it may seem the three fives remaining in the following `skeleton' are sufficient to reconstruct the entire long division sum.
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?
Explore the relationship between simple linear functions and their graphs.
Investigate the different ways these aliens count in this challenge. You could start by thinking about how each of them would write our number 7.
Who said that adding, subtracting, multiplying and dividing couldn't be fun?
Watch our videos of multiplication methods that you may not have met before. Can you make sense of them?
Choose two digits and arrange them to make two double-digit numbers. Now add your double-digit numbers. Now add your single digit numbers. Divide your double-digit answer by your single-digit answer. . . .
Powers of numbers behave in surprising ways. Take a look at some of these and try to explain why they are true.
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?
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.
A car's milometer reads 4631 miles and the trip meter has 173.3 on it. How many more miles must the car travel before the two numbers contain the same digits in the same order?
Replace each letter with a digit to make this addition correct.
This addition sum uses all ten digits 0, 1, 2...9 exactly once. Find the sum and show that the one you give is the only possibility.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
How many positive integers less than or equal to 4000 can be written down without using the digits 7, 8 or 9?
Choose any 3 digits and make a 6 digit number by repeating the 3 digits in the same order (e.g. 594594). Explain why whatever digits you choose the number will always be divisible by 7, 11 and 13.
The number 3723(in base 10) is written as 123 in another base. What is that base?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Can you show that 1^99 + 2^99 + 3^99 + 4^99 + 5^99 is divisible by 5?
When asked how old she was, the teacher replied: My age in years is not prime but odd and when reversed and added to my age you have a perfect square...
A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.
Consider all of the five digit numbers which we can form using only the digits 2, 4, 6 and 8. If these numbers are arranged in ascending order, what is the 512th number?
How many six digit numbers are there which DO NOT contain a 5?