Eugene wrote a 100 numbers on a board. He added 1 to each number and the product didn't change. He did the same thing k times, each time the product didn't change. What is the maximum k?
I guess the answer is 99 and that happens if the numbers are 99, 98, 97, 96,..., 0. But how do you rigorously prove it? Stuck on it for about an hour. Tried induction with 2, 3, 4 numbers