[kurto]

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First figure out the heaviest one just doing a binary search: 15 weighings. The key point is that the second heaviest coin is one that was eliminated by the winner at some point;

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Umm... correct me if I'm wrong here... but this doesn't always work.

If on the first trial, you compare the heaviest and the second heaviest... at the end of the first 15 weighings, you will only know which coin is the heaviest.

If you luck was bad and you had the 2nd heaviest when you started the second trial, it would take 14 weighings doing this method to find the next heaviest.

Worst case scenario... you could have to do 15+14+13+12= 54 weighings to determine the top 4 if, each time you start the trials, you begin with the heaviest.

Or am I missing something?