If the goal is to find the smallest sum, and if the digit 0 is ignored (as it is in the first row), then you could change 888 to 800, 777 to 700, 666 to 600, 555 to 500, 444 to 400, 333 to 300, 222 to 200, and 111 to 100. Tom Éric Angelini writes:
Hello Math-Fun, no cell of the hereunder triangle shares any of its digits with another cell of the same rank or column:
+-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 10 | 20 | 30 | 40 | 50 | 60 | 70 | 80 | 90 | +-----+-----+-----+-----+-----+-----+-----+-----+-----+ | 22 | 11 | 777 | 666 | 888 | 333 | 444 | 9 | +-----+-----+-----+-----+-----+-----+-----+-----+ | 33 | 8 | 555 | 111 | 222 | 47 | 69 | +-----+-----+-----+-----+-----+-----+-----+ | 44 | 3 | 1 | 59 | 67 | 28 | +-----+-----+-----+-----+-----+-----+ | 55 | 4 | 68 | 27 | 13 | +-----+-----+-----+-----+-----+ | 66 | 5 | 2 | 38 | +-----+-----+-----+-----+ | 77 | 6 | 49 | +-----+-----+-----+ | 88 | 7 | +-----+-----+ | 99 | +-----+
The cell with 68, for instance, doesn't share a 6 or a 8 with a cell above it, below it, on its right or left. Can you beat this triangle-- in terms of "sum of its 45 integers"? (I have 5451 here, I guess) Best, É.