Filter by: Content type: ALL Problems Articles Games Stage: All Stage 1&2 Stage 2&3 Stage 3&4 Stage 4&5 Challenge level:
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?"
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. . . .
How many different shaped boxes can you design for 36 sweets in one layer? Can you arrange the sweets so that no sweets of the same colour are next to each other in any direction?
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" .
Can you make square numbers by adding two prime numbers together?
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.
An investigation that gives you the opportunity to make and justify predictions.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
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 find any perfect numbers? Read this article to find out more...
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
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 the clues to find the mystery number.
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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 work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
56 406 is the product of two consecutive numbers. What are these two numbers?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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?
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 five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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.
What is the smallest number with exactly 14 divisors?
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!
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 complete this jigsaw of the multiplication square?
What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?
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?
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.
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.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
Can you find a way to identify times tables after they have been shifted up?
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?
When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
"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 ...?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A game that tests your understanding of remainders.
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 smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?