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. . . .
If you have only four weights, where could you place them in order
to balance this equaliser?
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!
Given the products of adjacent cells, can you complete this Sudoku?
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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.
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.
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...
Suppose we allow ourselves to use three numbers less than 10 and
multiply them together. How many different products can you find?
How do you know you've got them all?
This big box multiplies anything that goes inside it by the same number. If you know the numbers that come out, what multiplication might be going on in the box?
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?
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?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
56 406 is the product of two consecutive numbers. What are these
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 work out the arrangement of the digits in the square so
that the given products are correct? The numbers 1 - 9 may be used
once and once only.
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 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.
Can you work out what a ziffle is on the planet Zargon?
On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?
Can you make square numbers by adding two prime numbers together?
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
A game in which players take it in turns to choose a number. Can you block your opponent?
Can you complete this jigsaw of the multiplication square?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
The discs for this game are kept in a flat square box with a square
hole for each disc. Use the information to find out how many discs
of each colour there are in the box.
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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?
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.
Follow the clues to find the mystery number.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
Given the products of diagonally opposite cells - can you complete
How many different shaped boxes can you design for 36 sweets in one
layer? Can you arrange the sweets so that no sweets of the same
colour are next to each other in any direction?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
An environment which simulates working with Cuisenaire rods.
There is a clock-face where the numbers have become all mixed up. Can you find out where all the numbers have got to from these ten statements?
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?
A game that tests your understanding of remainders.
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?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
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?