A game that tests your understanding of remainders.
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?"
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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. . . .
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
Can you find a way to identify times tables after they have been shifted up?
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?
What is the smallest number of answers you need to reveal in order
to work out the missing headers?
Follow this recipe for sieving numbers and see what interesting patterns emerge.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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 with exactly 14 divisors?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
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?
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!
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Given the products of adjacent cells, can you complete this Sudoku?
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?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Can you complete this jigsaw of the multiplication square?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
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.
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 I. . . .
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
If you have only four weights, where could you place them in order
to balance this equaliser?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find the highest power of 11 that will divide into 1000! exactly.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?
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