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In the episode 'A Study in Pink' of the first season of Sherlock the victims are poisoned when forced to choose a pill from the two bottles as confessed by the cab driver. However in the earlier scenes the victims are shown to be picking a pill from the bottle which had multiple pills (3-4 pills). But when the cabbie forces Sherlock Holmes to choose from one of the bottles then each of the bottles had 1 pill only.

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Did the serial killer played different games with all his victims and Sherlock or the victims did not really have a choice as all the pills may have been poisonous. Why the number of pills were different?

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It's been awhile since I watched the episode, but I believe the simple answer comes down to the viewer not seeing the two bottles of pills side by side. The way the cabbie played the 'game', he presented two bottles of pills to each victim, with the idea that he'd take a pill from the other bottle (this was how he was playing the game with Sherlock). So while we see the victim take a pill from A bottle, we don't see what happens to the other pill bottle. The cabbie would take the pill from the other pill bottle, resulting in one pill remaining for his test with Sherlock (I'm presuming that if the cabbie had succeeded in killing Sherlock, he'd have simply kept going with a new set of pills - most likely provided for by Moriarty, seeing as how Moriarty was bankrolling him).

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  • It means that there is a possibility that no of pins denote the number of targets remaining for the cabbie and Sherlock was the last one.
    – Qrious
    Commented Jun 12, 2013 at 11:25
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I don't think the number of pills matters, because there are plenty of poisons that can kill with just one pill. For example, a lethal dose of potassium cyanide is only 300 mg. The real plot problem is that the cabbie killed four people (not three) before meeting Sherlock, and if the pill selection was random this means he had 0.5 * 0.5 * 0.5 * 0.5 = 0.0625 or a 6.25% chance of surviving that far. His chance of killing Sherlock drops to 3% and I don't think his sponsor (Moriarty) is the kind of guy to put a plan in motion that has a 1 in 32 chance of succeeding. In addition the cabbie is motivated to survive in order to make more money for his family. For these reasons the game must have been rigged. How? Potassium cyanide is a lethal poison that has a number of antidotes (i.e. hydroxocobalamin and a new one called sulfanegen triethanolamine). These antidotes are usually administered after cyanide poisoning and when present in the blood they convert cyanide to a harmless byproduct. So the cabbie could have put poison in both vials, self-administered a large dose of antidote before taking the cyanide and another large dose immediately after.

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There are the same number of pills in each bottle. All the pills in one bottle are poisoned. All the pills in the other bottle are not. The victims only choose the bottle. Once they've chosen the bottle, all the pills in the bottle are the same (either all poisoned or all benign, depending which bottle they picked).

With each victim, a pair of pills is consumed: one from the poisoned bottle and one from the non-poisoned. (Obviously, the cabbie takes a pill from the non-poisoned bottle each time.)

By the time it gets to Sherlock, there is only one pill left in each bottle, because all the others have been consumed. This doesn't change the game at all: he's still choosing the poisoned bottle or the non-poisoned bottle.

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  • That's correct and similar to Barry's answer. The bad bottle contained poisoned pill and the good bottle contained harmless one.
    – Qrious
    Commented Jun 4, 2014 at 10:55

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