You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
The clues for this Sudoku are the product of the numbers in adjacent squares.
Given the products of diagonally opposite 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. . . .
Given the products of adjacent cells, can you complete this Sudoku?
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?
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 complete this jigsaw of the multiplication square?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
What is the remainder when 2^2002 is divided by 7? What happens
with different powers of 2?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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" .
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!
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
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.
Can you work out what size grid you need to read our secret message?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?
A game that tests your understanding of remainders.
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.
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?
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?
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?
Follow the clues to find the mystery number.
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?"
A game in which players take it in turns to choose a number. Can you block your opponent?
For this challenge, you'll need to play Got It! Can you explain the strategy for winning this game with any target?
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
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.
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?
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?
Use the interactivities to complete these Venn diagrams.
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?
Use the interactivity to create some steady rhythms. How could you
create a rhythm which sounds the same forwards as it does
Find the highest power of 11 that will divide into 1000! exactly.
An investigation that gives you the opportunity to make and justify
Can you find any perfect numbers? Read this article to find out more...
Complete the following expressions so that each one gives a four
digit number as the product of two two digit numbers and uses the
digits 1 to 8 once and only once.
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?
Helen made the conjecture that "every multiple of six has more
factors than the two numbers either side of it". Is this conjecture
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?
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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.
How many integers between 1 and 1200 are NOT multiples of any of
the numbers 2, 3 or 5?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
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.
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?