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. . . .
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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.
Got It game for an adult and child. How can you play so that you know you will always win?
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?
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?
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!
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Given the products of diagonally opposite cells - can you complete this Sudoku?
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?
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
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?
A game that tests your understanding of remainders.
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 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 complete this jigsaw of the multiplication square?
The clues for this Sudoku are the product of the numbers in adjacent squares.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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?
Follow the clues to find the mystery number.
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.
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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
A game in which players take it in turns to choose a number. Can you block your opponent?
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 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.
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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 for 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?
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?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
An environment which simulates working with Cuisenaire rods.
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?
Factors and Multiples game for an adult and child. How can you make sure you win this game?
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?
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?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
Can you work out some different ways to balance this equation?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?