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. . . .
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.
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!
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?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
If you have only four weights, where could you place them in order
to balance this equaliser?
Can you complete this jigsaw of the multiplication square?
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 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.
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
When the number x 1 x x x is multiplied by 417 this gives the
answer 9 x x x 0 5 7. Find the missing digits, each of which is
represented by an "x" .
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
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 2 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
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 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?
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 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?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
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.
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
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 the number which has 8 divisors, such that the product of the
divisors is 331776.
Can you work out some different ways to balance this equation?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
I'm thinking of a number. When my number is divided by 5 the
remainder is 4. When my number is divided by 3 the remainder is 2.
Can you find my number?
Got It game for an adult and child. How can you play so that you know you will always win?
A game that tests your understanding of remainders.
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
An environment which simulates working with Cuisenaire rods.
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?
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?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
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...
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?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?