Three identical, mute triplets, $F$, $S$, and $T$, each of whom is a perfect logician, have been kidnapped. Their captor begins by instructing them that in a room that they will shortly enter, are six wine goblets, three of which contain normal wine, and three of which are poisoned. The poison is such that once even a drop is drunk, ten seconds later, they will die; but is of course otherwise indistinguishable from the wine. They are told that each person must drink from one glass; they may choose to drink all of it, or just take a sip (and their survival does not depend how much they drink).
To make things more interesting, the captor takes $F$ into the room, and truthfully points out which three are poisoned. They leave the room. The platter on which the six wine glasses are on then spins an unknown amount.
$F$ enters the room, selects a glass, and drinks all of its contents. You know that $F$ fully drunk the glass, while the others do not.
After enough time for the poison to take effect (if $F$ had been poisoned), $S$ enters the room, sees if $F$ is alive or dead, selects a glass, and either drinks all of or takes a sip from it.
After enough time for the poison to take effect (if $S$ had been poisoned), $T$ enters the room, sees if $F$ and $S$ are alive or dead, selects a glass, and either drinks all of or takes a sip from it.
Fifteen seconds later, exactly one person lies dead on the floor.
The state of the platter is shown below, where a white circle represents an empty glass, and a purple circle shows a full (or sipped-from) glass. Note how the glasses are in groups of two around the edge, these are indented to be equally spaced.
Puzzle: Which triplet, $F$, $S$, or $T$, was poisoned?
There's no lateral-thinking tag, it's a purely logical puzzle. So, you can assume that:
- no communication occurred
- the glasses are all identical
- the glasses' relative positions do not shift during the rotation
- each person has perfect logical capabilities and memory
- none of them are suicidal
- only $F$ saw the glasses
- you cannot tell the difference between a full and sipped-from glass
- when $T$ enters he is unsure if it was $F$ or $S$ who sipped and who emptied
- the glass were left in the positions they were taken from
- each person does not care if the others survive; they have no priorities other than surviving themselves
If in doubt, feel free to ask.
Puzzle created by me; I have the solution.