The Pill Puzzle
 
AuthorMessage
zak
19 Apr 2017 12:46 AM
Since there was some critique on my solution to the pill puzzle (known from the main Chat Box), I post my solution again in the forum for better readability. I also put steps 1b and c to the end of the list of the regular 4 steps, which hopefully makes it less confusing to read. Here it is:
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Step 1: You put 5 pills aside and weigh the remaining 30, fifteen on either side of the scale. If they are level, the lighter placebo must be among the 5 pills on the table. In that case, you proceed with steps 1b and c. If one of the pans goes up, the lighter placebo must be in that pan. You put the 15 pills from the pan that went down to the other 5 pills on the table and one pill from the pan that went up seperately on the table.

Step 2: Now you spread the remaining 14 pills evenly to the two pans, now weighing 7 against 7. If they are level, the lighter placebo must be the one pill you put seperately on the table. If one of the pans goes up, the lighter placebo must be in that pan. So you discard the 7 pills from the heavy pan and put one pill from the light pan seperately on the table.

Step 3: Now you spread the remaining 6 pills evenly to the two pans, now weighing 3 against 3. If they are level, the lighter placebo must be the one pill you put seperately on the table last time. If one of the pans goes up, the lighter placebo must be in that pan. So you discard the 3 pills from the heavy pan and put one pill from the light pan seperately on the table.

Step 4: Now you spread the remaining 2 pills evenly to the two pans, now weighing 1 against 1. If they are level, the lighter placebo must be the one pill you put seperately on the table last time. If one of the pans goes up, the lighter placebo must be the one pill in that pan. BINGO in 4 steps!


Steps 1b and c: You take the 5 pills from the table, put one pill seperately back on the table and spread the remaining 4 pills evenly to the pans, now weighing 2 against 2. If they are level, the lighter placebo must be the one pill you put seperately on the table. BINGO in 2 steps! If one of the pans goes up, the lighter placebo must be in that pan. So you discard the 2 pills from the heavy pan and weigh the remaining two pills from the light pan against each other. The pill in the lighter pan must be the placebo. BINGO in 3 steps!
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I still think this is a 100% certain way to find the placebo pill in 2 steps if you are extremely lucky, in 3 steps if you are lucky and in 4 steps on a regular day ;-). One way or another, you won't need more than 4 steps, as the rule demands.
bob440
19 Apr 2017 6:55 AM
I think the puzzle as originally posed stated that one doesn't know whether the poison pill is lighter or heavier -- only that it is different than all the others
zak
21 Apr 2017 5:08 AM
The puzzle works both ways, but the game master has to decide which it should be (and tell the contestant) before the weighing starts.
zak
21 Apr 2017 2:48 AM
For those who missed it, here is the pill puzzle as presented in the main chat box earlier:

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You have 35 numbered pills of equal size and look, only one of them, the placebo, is a bit lighter than the other 34. Find the placebo with no more than 4 weighings in a two-pan-scale.
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