Hi.
I was trying to solve this problem. Here is the problem link.
If n = 4, k = 0, the apples are of weight 1, 2, 3, 4.
If he eats apple #1:
If apple #1 is sweet, then he must eat apples of total weight 1.
If apple #2 is sweet, then the total weight is 3.
If apple #3 is sweet, then the total weight is 6.
If apple #4 is the sweet one, then he must must eat apples of total weight 6 also.(because he will know the answer regardless of the taste of apple #3)
Then we have total answer of: 1 + 3 + 6 + 6 = 16.
Why the answer in this case is equal to 13?
Thanks in advance.
The best giant strategy in this case is to eat the first apple, then, if necessary, to eat the third apple:
If apple #1 is sweet he will eat only the first one -> total weight = 1
If apple #2 is sweet he will eat the first (bitter) then the third (sour) — so he now know the second one is sweet -> total weight = 4
If apple #3 is sweet he will eat the first (bitter) then the third (sweet) -> total weight = 4
If apple #4 is sweet he will eat the first (bitter) then the third (bitter) -> total weight = 4
So the answer is (it is actually misprinted in the statement as "1+3+3+3=13")
1 + 4 + 4 + 4 = 13