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?"
Given the products of adjacent 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.
Given the products of diagonally opposite cells - can you complete this Sudoku?
If you have only four weights, where could you place them in order
to balance this equaliser?
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!
Can you complete this jigsaw of the multiplication square?
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?
Arrange the four number cards on the grid, according to the rules,
to make a diagonal, vertical or horizontal line.
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.
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?
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?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
The clues for this Sudoku are the product of the numbers in adjacent squares.
An environment which simulates working with Cuisenaire rods.
For this challenge, you'll need to play Got It! Can you explain the
strategy for winning this game with any target?
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?
A game in which players take it in turns to choose a number. Can you block your opponent?
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.
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 game that tests your understanding of remainders.
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?
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 fill in this table square? The numbers 2 -12 were used to
generate it with just one number used twice.
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 people using a pack of cards Turn over 2 cards and try
to make an odd number or a multiple of 3.
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.
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?
Follow the clues to find the mystery number.
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.
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Use the interactivities to complete these Venn diagrams.
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.
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.
What is the smallest number with exactly 14 divisors?
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?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
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
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
Can you predict when you'll be clapping and when you'll be clicking
if you start this rhythm? How about when a friend begins a new
rhythm at the same time?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
An investigation that gives you the opportunity to make and justify
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?