This might be what Hashman was saying, but we know that if we got rid of the absolute values, then the total sum would always be 0 (we'd just be subtracting the sum of a non-permuted array from the sum of a permuted array). So, if we categorize the value of each difference (in the non-absolute value case) as either "positive," "negative," or "zero," we know that the positive and negative equal each other in magnitude. Thus, when we throw the abs-vals back in to get the problem statement, we know that the total sum must be even.