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?
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.
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.
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
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?
What is the smallest number with exactly 14 divisors?
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?
Rectangles are considered different if they vary in size or have different locations. How many different rectangles can be drawn on a chessboard?
Caroline and James pick sets of five numbers. Charlie chooses three of them that add together to make a multiple of three. Can they stop him?
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. . . .
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
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 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 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 find a way to identify times tables after they have been shifted up?
The clues for this Sudoku are the product of the numbers in adjacent squares.
Is it possible to draw a 5-pointed star without taking your pencil
off the paper? Is it possible to draw a 6-pointed star in the same
way without taking your pen off?
A game that tests your understanding of remainders.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Given the products of diagonally opposite 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...
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?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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?"
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. . . .
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Got It game for an adult and child. How can you play so that you know you will always win?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.