Find four distinct integers a,b,c,d such that 100 <= a,b,c,d <= 12000 and the sum of "all" the four of them and the sum of "every" two of them are perfect squares. (That is, a+b, a+c, a+d, b+c, b+d, c+d, and a+b+c+d are all squares of integers.) ---------------------- Squares between 200 and 24000 -> integers between 14 and 154 Big square between 400 and 48000 -> integers between 20 and 219 => Range between 14 and 219 => (219 - 14 + 1) ^ 4 = 1800814096 possibilities => brute force impossible