Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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.
56 406 is the product of two consecutive numbers. What are these
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.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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?
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?
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. . . .
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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?
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.
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?
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?
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
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 can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
What is the smallest number with exactly 14 divisors?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you find a way to identify times tables after they have been shifted up?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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.
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
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.
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 game in which players take it in turns to choose a number. Can you block your opponent?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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 fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
Using the digits 1, 2, 3, 4, 5, 6, 7 and 8, mulitply a two two
digit numbers are multiplied to give a four digit number, so that
the expression is correct. How many different solutions can you
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?
An investigation that gives you the opportunity to make and justify
Can you find any perfect numbers? Read this article to find out more...
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.
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?