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Pastimes : Brain Teasers.
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To: Mitch Blevins who wrote (110)3/4/1998 1:52:00 AM
From: space cadet  Read Replies (1) of 136
 
I think you're on the right track but I don't quite follow you. Does your formula work for n=12 and k=3? I'm pretty certain 13 balls requires 4 weighings. As I remember it my friends proof of the correct formula (and I forget the exact formula though I probably do still have it in my possession somewhere) required several pages. I think the tricky thing was figuring out when the number of weighings must jump like it does from 12 to 13 balls. Probably you can figure it out by induction, as it seems you are trying to do. I remember my friend actually thought the formula was useful for something halfway practical, but now I can't remember what it was.
Right you are that after the first weighing you always have a control ball. Of course, that is the key to the puzzle, and the fact that most people never figure out. You can't believe how many people have told me the puzzle can't be solved because of that.
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