Sherlockian Deduction versus Criminal Mastermind
A murderous super-villain that praises himself on leaving seemingly improbable to solve puzzles left as clues on his crime scenes, left a coded device with the whereabouts of his next victim that he poisoned with a lethal poison that will take an effect in 30 minutes with a message above denoting that you have 10 minutes to find out his location and 20 minutes to get there and administer the antidote, the code is a ten-digit code and even with the best super-computers you won't be able to find it in several hours, so instead he sent his henchman to give you a practical puzzle, and if you can solve it, he will give you the code, and you will find the location.
But what about the antidote? The antidote is in the puzzle: The henchman presents you with 5 big jars, each filled with a great number of same shape and size and same looking pills, equally filled, 4 of the jars are filled with placebo pills weighing 10 grams each and 1 of the jar is filled with antidote pills weighing 9 grams each.
The henchman presents you with a weighing scale and a sets you with a requirement to do the minimum amount of weighing (weighing=any amount of jars or pills place to be weight at once on the weighing scale) on the weighing scale to determine which jar is the one with the antidotes.
(The henchman is one of the top marksmen in the underworld and holds you on a gunpoint so there'll be no chances of you trying any funny business and stealing or crashing the pills, so for all intents and purposes it is impossible for you to steal one pill from each jar.)
What is the minimum amount of weighing to guarantee that you will determine the jar with the antidotes, get the code and hence save the potential victim? (if you correctly do it with the minimum possible weighing, the henchman will give you the code, but if you don't you only have the antidote which makes it useless if you don't have the code to the location) Think about what strategy will you use. (hint: think outside of the jar)
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Take a different number of pills from each jar and compare the expected mass with the observed mass. For instance, take:
1 pill from jar 1 2 pills from jar 2 3 pills from jar 3 4 pills from jar 4 5 pills from jar 5 Expected mass (if all pills were 10 grams each) = (1+2+3+4+5) * 10 = 150 grams.
Suppose jar 4 contained the 9 gram pills. The total mass that you observe would be (1+2+3+5) * 10 + 4*9 = 146 grams. Since the mass you observe is 4 grams less than the expected 150 grams, you know jar 4 is holding the 9 gram pills.
In general (using the distribution of pills from above):
Jar # = | Expected mass (150g) - observed mass |