### There are 17 results

Broad Topics >

Numbers and the Number System > Integers

##### Age 16 to 18 Challenge Level:

The symbol [ ] means 'the integer part of'. Can the numbers [2x];
2[x]; [x + 1/2] + [x - 1/2] ever be equal? Can they ever take three
different values?

##### Age 14 to 16 Challenge Level:

Find the maximum value of 1/p + 1/q + 1/r where this sum is less than 1 and p, q, and r are positive integers.

##### Age 14 to 16 Challenge Level:

To make 11 kilograms of this blend of coffee costs £15 per
kilogram. The blend uses more Brazilian, Kenyan and Mocha coffee...
How many kilograms of each type of coffee are used?

##### Age 14 to 18 Challenge Level:

Find the smallest integer solution to the equation 1/x^2 + 1/y^2 = 1/z^2

##### Age 16 to 18 Challenge Level:

Explore the properties of some groups such as: The set of all real
numbers excluding -1 together with the operation x*y = xy + x + y.
Find the identity and the inverse of the element x.

##### Age 14 to 16 Challenge Level:

A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?

##### Age 14 to 16 Challenge Level:

I am exactly n times my daughter's age. In m years I shall be ... How old am I?

##### Age 14 to 16 Challenge Level:

Can you explain why a sequence of operations always gives you perfect squares?

##### Age 14 to 16 Challenge Level:

Euler found four whole numbers such that the sum of any two of the numbers is a perfect square...

##### Age 11 to 16 Challenge Level:

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?

##### Age 14 to 16 Challenge Level:

If a two digit number has its digits reversed and the smaller of the two numbers is subtracted from the larger, prove the difference can never be prime.

##### Age 14 to 16 Challenge Level:

Explore the factors of the numbers which are written as 10101 in
different number bases. Prove that the numbers 10201, 11011 and
10101 are composite in any base.

##### Age 14 to 16 Challenge Level:

Show that if you add 1 to the product of four consecutive numbers
the answer is ALWAYS a perfect square.

##### Age 7 to 18

Ranging from kindergarten mathematics to the fringe of research
this informal article paints the big picture of number in a non
technical way suitable for primary teachers and older students.

##### Age 14 to 16 Challenge Level:

Can you create a Latin Square from multiples of a six digit number?

##### Age 16 to 18

How can we solve equations like 13x + 29y = 42 or 2x +4y = 13 with
the solutions x and y being integers? Read this article to find
out.

##### Age 7 to 16 Challenge Level:

Using the 8 dominoes make a square where each of the columns and rows adds up to 8