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 clues for this Sudoku are the product of the numbers in adjacent squares.
Follow the clues to find the mystery number.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you make square numbers by adding two prime numbers together?
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.
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
How many numbers less than 1000 are NOT divisible by either: a) 2 or 5; or b) 2, 5 or 7?
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.
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?
The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?
An investigation that gives you the opportunity to make and justify predictions.
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?
An environment which simulates working with Cuisenaire rods.
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. . . .
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.
Complete the magic square using the numbers 1 to 25 once each. Each row, column and diagonal adds up to 65.
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Can you find a way to identify times tables after they have been shifted up?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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?
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?
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?"
Can you find any perfect numbers? Read this article to find out more...
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.
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!
What is the smallest number with exactly 14 divisors?
Find the highest power of 11 that will divide into 1000! exactly.
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. . . .
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.
The five digit number A679B, in base ten, is divisible by 72. What are the values of A and B?
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?
Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?
I am thinking of three sets of numbers less than 101. Can you find all the numbers in each set from these clues?
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?
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...
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Which pairs of cogs let the coloured tooth touch every tooth on the other cog? Which pairs do not let this happen? Why?
A game that tests your understanding of remainders.