The clues for this Sudoku are the product of the numbers in adjacent squares.
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. . . .
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?"
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
A game that tests your understanding of remainders.
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?
Given the products of adjacent cells, can you complete this Sudoku?
6! = 6 x 5 x 4 x 3 x 2 x 1. The highest power of 2 that divides
exactly into 6! is 4 since (6!) / (2^4 ) = 45. What is the highest
power of two that divides exactly into 100!?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
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" .
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
What is the smallest number with exactly 14 divisors?
What is the value of the digit A in the sum below: [3(230 + A)]^2 =
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?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
Do you know a quick way to check if a number is a multiple of two? How about three, four or six?
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?
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?
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?
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Follow the clues to find the mystery number.
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.
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.
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
Make a set of numbers that use all the digits from 1 to 9, once and
once only. Add them up. The result is divisible by 9. Add each of
the digits in the new number. What is their sum? Now try some. . . .
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
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
Twice a week I go swimming and swim the same number of lengths of the pool each time. As I swim, I count the lengths I've done so far, and make it into a fraction of the whole number of lengths I. . . .
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?
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...
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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?
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
An investigation that gives you the opportunity to make and justify
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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?
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.
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?
Can you find any perfect numbers? Read this article to find out more...
Can you find a way to identify times tables after they have been shifted up?
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?
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?