discrete math help!!!?
the intergers 1-10 inclusive are placed around a circle in a random order...show that whatever the order there are always 3 consecutive numbers whose sum is at least 17
i think its the pigeonhole principle but i don't know how to do it
- 1 decade agoFavorite Answer
The sum of all 3 consecutive numbers is
Since there are 10 different 3 consecutive numbers, if each of them were at most 16, then the sum of all 3 consecutive numbers would be at most
Since this is lower than the sum that we're supposed to get, there must be at least one(rather more than one) 3 consecutive numbers whose sum is at least 17.