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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
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?"
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?
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.
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!
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
If you have only four weights, where could you place them in order
to balance this equaliser?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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...
An environment which simulates working with Cuisenaire rods.
Can you complete this jigsaw of the multiplication square?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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 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.
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 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.
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?
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?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
A game in which players take it in turns to choose a number. Can you block your opponent?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Follow the clues to find the mystery number.
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
A game that tests your understanding of remainders.
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?
Given the products of diagonally opposite cells - can you complete
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?
What is the smallest number with exactly 14 divisors?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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?
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
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.
Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?
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?
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.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Use the interactivities to complete these Venn diagrams.