Eric, I like your triangular puzzle and wrote a program that improves existing solutions by swapping digits. A good approach is to put the digits "1" in the longest diagonal and digits "2" in the next one. A lower bound of the sum is exactly 6000. My best solution so far has a sum of 6073. To improve this solution the integers 50, 60 and 70 should be replaced by smaller integers. It is not possible to replace one of the numbers 111, 222, 333, ..., 999. 555, 666, 888, 444, 999, 70, 333, 222, 111 44, 777, 66, 8, 55, 39, 20, 1 77, 9, 3, 6, 40, 25, 18 99, 5, 7, 30, 26, 14 88, 4, 50, 27, 13 60, 38, 24, 15 33, 2, 19 22, 10 11 Sum = 6073 Walter Trump