
Same (Sum of) Differences  ProblemADay
Nice puzzle  pity this community seems to be dead now. Can't resist answering (I'm like in that xkcd cartoon  someone who can be immediately derailed by a mathematical puzzle, regardless of circumstances.)
The sum in question equals n^{2} when A = {1,...,n}. And the sum is unchanged whenever two adjacent numbers, one in A and the other in B, are 'flipped over'.

