What is the minimum number of times you must throw three fair six-sided dice to ensure that the same sum is rolled twice?
You can have 16 (3-18) total sums.
So worse case scenerio, you roll all 16 once, meaning that you have to roll 17 time to ensure that the same sum is rolled.
We can't say what the minimum number might be ( we COULD get the same sum on two consecutive rolls)
We have 16 different outcomes
However, by the pigeonhole principle, we can guarantee that we will get the SAME sum (at least once) after a maximum of 16 rolls after the initial result......so 17 total rolls