Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
Nearly all of us have made table patterns on hundred squares, that is 10 by 10 grids. This problem looks at the patterns on differently sized square grids.
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
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?
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.
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?
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?
Find the words hidden inside each of the circles by counting around a certain number of spaces to find each letter in turn.
56 406 is the product of two consecutive numbers. What are these two numbers?
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?
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 work out what a ziffle is on the planet Zargon?
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?
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.
These red, yellow and blue spinners were each spun 45 times in total. Can you work out which numbers are on each spinner?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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" .
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
A game that tests your understanding of remainders.
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.
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?
This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
A game in which players take it in turns to choose a number. Can you block your opponent?
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?"
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
Find the number which has 8 divisors, such that the product of the divisors is 331776.
Can you find any perfect numbers? Read this article to find out more...
Helen made the conjecture that "every multiple of six has more factors than the two numbers either side of it". Is this conjecture true?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
Can you find what the last two digits of the number $4^{1999}$ are?
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 = 49280A
I put eggs into a basket in groups of 7 and noticed that I could easily have divided them into piles of 2, 3, 4, 5 or 6 and always have one left over. How many eggs were in the basket?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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?
Find the highest power of 11 that will divide into 1000! exactly.
Can you find a relationship between the number of dots on the circle and the number of steps that will ensure that all points are hit?
Follow the clues to find the mystery number.
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Explore the relationship between simple linear functions and their graphs.