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?"
Given the products of adjacent cells, can you complete this Sudoku?
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.
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. . . .
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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?
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.
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.
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?
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 complete this jigsaw of the multiplication square?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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!
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
A game that tests your understanding of remainders.
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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.
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
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?
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?
An investigation that gives you the opportunity to make and justify
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
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?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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...
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?