Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?
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?
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?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you find what the last two digits of the number $4^{1999}$ are?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you find a way to identify times tables after they have been shifted up?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
This article for teachers describes how number arrays can be a useful reprentation for many number concepts.
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
Can you find any perfect numbers? Read this article to find out more...
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...
How many integers between 1 and 1200 are NOT multiples of any of the numbers 2, 3 or 5?
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?
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?
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Follow the clues to find the mystery number.
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?
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.
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
What is the smallest number with exactly 14 divisors?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Find some triples of whole numbers a, b and c such that a^2 + b^2 + c^2 is a multiple of 4. Is it necessarily the case that a, b and c must all be even? If so, can you explain why?
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Given the products of adjacent cells, can you complete this Sudoku?
Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.
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?
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. . . .
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?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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?
A game that tests your understanding of remainders.
An investigation that gives you the opportunity to make and justify predictions.
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 two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.
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.
Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?