This is the solution sent in by Yatir Halevi. Thanks Yatir. A correct solution was also received from Andrei Lazanu.

Let's say we want to find the square of a .

We know that a² = a²−b²+b² = (a+b)×(a−b)+b²

and for every a, we can pick a certain b that will make the calculation a² as easy as possible.

For instance if we take a=35 , we can take b=5 ,

we get 35²=(35+5)×(35−5)+5² = 40×30+25 = 1200+25 = 1225

So, if a is a number that ends with a 5: it can be written as

a=10×q + 5 a²=(10q+5)²=(10q+5−5)×(10q+5+5)+25=10q(10q+10)+25=10²q(q+1)+25 .

So a² is equal to q(q+1) plus two zeros after it (10²) that are "stolen" by the 25 that is added on.