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?
There are ten children in Becky's group. Can you find a set of
numbers for each of them? Are there any other sets?
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" .
Benâ€™s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
56 406 is the product of two consecutive numbers. What are these
How many different sets of numbers with at least four members can
you find in the numbers in this box?
What is the lowest number which always leaves a remainder of 1 when
divided by each of the numbers from 2 to 10?
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.
Explain why the arithmetic sequence 1, 14, 27, 40, ... contains many terms of the form 222...2 where only the digit 2 appears.
Can you find any perfect numbers? Read this article to find out more...
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. . . .
Follow the clues to find the mystery number.
An investigation that gives you the opportunity to make and justify
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?
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.
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 find?
These red, yellow and blue spinners were each spun 45 times in
total. Can you work out which numbers are on each spinner?
Andrew decorated 20 biscuits to take to a party. He lined them up and put icing on every second biscuit and different decorations on other biscuits. How many biscuits weren't decorated?
The five digit number A679B, in base ten, is divisible by 72. What
are the values of A and B?
Can you fill in this table square? The numbers 2 -12 were used to generate it with just one number used twice.
Work out Tom's number from the answers he gives his friend. He will
only answer 'yes' or 'no'.
Find the number which has 8 divisors, such that the product of the
divisors is 331776.
Norrie sees two lights flash at the same time, then one of them
flashes every 4th second, and the other flashes every 5th second.
How many times do they flash together during a whole minute?
What happens if you join every second point on this circle? How
about every third point? Try with different steps and see if you
can predict what will happen.
Katie and Will have some balloons. Will's balloon burst at exactly
the same size as Katie's at the beginning of a puff. How many puffs
had Will done before his balloon burst?
The planet of Vuvv has seven moons. Can you work out how long it is
between each super-eclipse?
Find the words hidden inside each of the circles by counting around
a certain number of spaces to find each letter in turn.
Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?
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?
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?
How can you use just one weighing to find out which box contains
the lighter ten coins out of the ten boxes?
The number 12 = 2^2 × 3 has 6 factors. What is the smallest natural number with exactly 36 factors?
Got It game for an adult and child. How can you play so that you know you will always win?
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?
Which is quicker, counting up to 30 in ones or counting up to 300 in tens? Why?
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?
This article for teachers describes how number arrays can be a
useful reprentation for many number concepts.
I throw three dice and get 5, 3 and 2. Add the scores on the three
dice. What do you get? Now multiply the scores. What do you notice?
Number problems at primary level to work on with others.
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?
Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?
Number problems at primary level that may require determination.
48 is called an abundant number because it is less than the sum of
its factors (without itself). Can you find some more abundant
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?
Does a graph of the triangular numbers cross a graph of the six
times table? If so, where? Will a graph of the square numbers cross
the times table too?
An environment which simulates working with Cuisenaire rods.
How many numbers less than 1000 are NOT divisible by either: a) 2
or 5; or b) 2, 5 or 7?