You are given the Lowest Common Multiples of sets of digits. Find
the digits and then solve the Sudoku.
Given the products of diagonally opposite cells - can you complete this Sudoku?
Follow the clues to find the mystery number.
An environment which simulates working with Cuisenaire rods.
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?"
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?
An investigation that gives you the opportunity to make and justify
Can you make square numbers by adding two prime numbers together?
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.
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 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?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
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?
Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Complete the magic square using the numbers 1 to 25 once each. Each
row, column and diagonal adds up to 65.
Can you work out some different ways to balance this equation?
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?
Have a go at balancing this equation. Can you find different ways of doing it?
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?
Investigate the smallest number of moves it takes to turn these
mats upside-down if you can only turn exactly three at a time.
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.
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?
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!
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?
A three digit number abc is always divisible by 7 when 2a+3b+c is divisible by 7. Why?
Imagine a wheel with different markings painted on it at regular
intervals. Can you predict the colour of the 18th mark? The 100th
Can you complete this jigsaw of the multiplication square?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
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?
Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.
Given the products of adjacent cells, can you complete this Sudoku?
If you have only four weights, where could you place them in order
to balance this equaliser?
Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?
When Charlie asked his grandmother how old she is, he didn't get a
straightforward reply! Can you work out how old she is?
Which pairs of cogs let the coloured tooth touch every tooth on the
other cog? Which pairs do not let this happen? Why?
"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?
Imagine we have four bags containing a large number of 1s, 4s, 7s and 10s. What numbers can we make?
Are these statements always true, sometimes true or never true?
Imagine we have four bags containing numbers from a sequence. What numbers can we make now?
Look at three 'next door neighbours' amongst the counting numbers. Add them together. What do you notice?
I am thinking of three sets of numbers less than 101. Can you find
all the numbers in each set from these clues?
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?
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.
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?
Can you find any perfect numbers? Read this article to find out more...
Number problems at primary level that may require determination.
Number problems at primary level to work on with others.
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.