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 that tests your understanding of remainders.
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
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. . . .
Can you work out what a ziffle is on the planet Zargon?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
List any 3 numbers. It is always possible to find a subset of
adjacent numbers that add up to a multiple of 3. Can you explain
why and prove it?
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
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...
Can you complete this jigsaw of the multiplication square?
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
Find some examples of pairs of numbers such that their sum is a
factor of their product. eg. 4 + 12 = 16 and 4 × 12 = 48 and
16 is a factor of 48.
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.
Use the interactivities to complete these Venn diagrams.
Can you find a way to identify times tables after they have been shifted up?
Choose any 3 digits and make a 6 digit number by repeating the 3
digits in the same order (e.g. 594594). Explain why whatever digits
you choose the number will always be divisible by 7, 11 and 13.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
What is the smallest number with exactly 14 divisors?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Got It game for an adult and child. How can you play so that you know you will always win?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
Take any two digit number, for example 58. What do you have to do to reverse the order of the digits? Can you find a rule for reversing the order of digits for any two digit number?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
If you have only four weights, where could you place them in order
to balance this equaliser?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
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!
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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 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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
Given the products of adjacent cells, can you complete this Sudoku?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
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?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
A game in which players take it in turns to choose a number. Can you block your opponent?
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?