If you have only four weights, where could you place them in order
to balance this equaliser?
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. . . .
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.
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?"
Given the products of adjacent cells, can you complete this Sudoku?
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...
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?
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!
Can you complete this jigsaw of the multiplication square?
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.
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.
Can you work out what a ziffle is on the planet Zargon?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
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?
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?
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.
Can you make square numbers by adding two prime numbers together?
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.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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?
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?
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
A game in which players take it in turns to choose a number. Can you block your opponent?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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?
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 sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
A game that tests your understanding of remainders.
An environment which simulates working with Cuisenaire rods.
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?
An investigation that gives you the opportunity to make and justify
"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
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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?
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?
Each light in this interactivity turns on according to a rule. What
happens when you enter different numbers? Can you find the smallest
number that lights up all four lights?
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 lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?