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?
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. . . .
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...
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.
Follow the clues to find the mystery number.
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?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Some 4 digit numbers can be written as the product of a 3 digit
number and a 2 digit number using the digits 1 to 9 each once and
only once. The number 4396 can be written as just such a product.
Can. . . .
What is the smallest number with exactly 14 divisors?
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!
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
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
A game that tests your understanding of remainders.
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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?
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?
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?
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.
If you have only four weights, where could you place them in order
to balance this equaliser?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
Do you know a quick way to check if a number is a multiple of two?
How about three, four or six?
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.
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?
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?
Can you find a way to identify times tables after they have been shifted up?
In this activity, the computer chooses a times table and shifts it.
Can you work out the table and the shift each time?
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?
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?
Given the products of diagonally opposite cells - can you complete
Can you complete this jigsaw of the multiplication square?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
An investigation that gives you the opportunity to make and justify
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?
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?
Can you fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you make square numbers by adding two prime numbers together?
A number N is divisible by 10, 90, 98 and 882 but it is NOT
divisible by 50 or 270 or 686 or 1764. It is also known that N is a
factor of 9261000. What is N?
I put eggs into a basket in groups of 7 and noticed that I could
easily have divided them into piles of 2, 3, 4, 5 or 6 and always
have one left over. How many eggs were in the basket?