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?"
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
Given the products of adjacent cells, can you complete this Sudoku?
Given the products of diagonally opposite cells - can you complete this Sudoku?
If you take a three by three square on a 1-10 addition square and
multiply the diagonally opposite numbers together, what is the
difference between these products. Why?
Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?
Find the smallest whole number which, when mutiplied by 7, gives a
product consisting entirely of ones.
In the multiplication calculation, some of the digits have been replaced by letters and others by asterisks. Can you reconstruct the original multiplication?
The clues for this Sudoku are the product of the numbers in adjacent squares.
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 letters in the following addition sum represent the digits 1
... 9. If A=3 and D=2, what number is represented by "CAYLEY"?
If these elves wear a different outfit every day for as many days
as possible, how many days can their fun last?
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?
Seven friends went to a fun fair with lots of scary rides. They
decided to pair up for rides until each friend had ridden once with
each of the others. What was the total number rides?
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?
Each clue number in this sudoku is the product of the two numbers in adjacent cells.
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
This multiplication uses each of the digits 0 - 9 once and once only. Using the information given, can you replace the stars in the calculation with figures?
Find the values of the nine letters in the sum: FOOT + BALL = GAME
Use the clues to work out which cities Mohamed, Sheng, Tanya and
Bharat live in.
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Number problems at primary level that require careful consideration.
There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.
The number of plants in Mr McGregor's magic potting shed increases
overnight. He'd like to put the same number of plants in each of
his gardens, planting one garden each day. How can he do it?
A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.
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?
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?
You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
How could you put these three beads into bags? How many different ways can you do it? How could you record what you've done?
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?
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.
This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.
Only one side of a two-slice toaster is working. What is the
quickest way to toast both sides of three slices of bread?
Make a pair of cubes that can be moved to show all the days of the
month from the 1st to the 31st.
Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
Can you replace the letters with numbers? Is there only one
solution in each case?
What do the digits in the number fifteen add up to? How many other
numbers have digits with the same total but no zeros?
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?
Follow the clues to find the mystery number.
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.
How many ways can you find to do up all four buttons on my coat?
How about if I had five buttons? Six ...?
A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.
Lolla bought a balloon at the circus. She gave the clown six coins
to pay for it. What could Lolla have paid for the balloon?
In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?
Two sudokus in one. Challenge yourself to make the necessary
These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.