Professor X has managed to create a simple programme that can multiply any two whole numbers and calculate the answer correctly.
But, a problem has arisen; it seems the programme will not correctly multiply a number by itself (such as 4 X 4).
Fortunately, the professor knows a way to get around this glitch.
Keeping in mind that the programme must accept any whole integer, do you know a way to have the programme multiply the numbers in a different way to get the correct result?
This method only has to work when multiplying a number by itself.
Answer
Here’s a neat trick to calculate any given number multiplied by itself:
Take one less than the given number and multiply it by one greater than the given number and add 1.
For example:
25 X 25 = 625
24 X 26 = 624 + 1 = 625
It also works for negative numbers:
-1 X -1 = 1
-2 X 0 + 1 = 1
The mathematical formula that the professor should use would be:
(n = given integer)
(n + 1) X (n—1) + 1
This would be equivalent to n X n.
