## Challenge 270: Squared Differences

If I pick three distinct integers – let’s say a, b and c – and calculate the sum of the squares of their differences:

(a – b)^{2} + (b – c)^{2} + (c – a)^{2}

what is the least possible value I can obtain?

What is the least possible value if I double the number of distinct integers to six (a, b, c, d ,e and f), and calculate the sum of these six differences?

(a – b)^{2} + (b – c)^{2} + (c – d)^{2} + (d – e)^{2} + (e – f)^{2} + (f – a)^{2}