Soda machine

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This is a quite old puzzle, although this version was inspired by a recent post on Richard Wiseman's Blog.


You have an old soda vending machine used in blind taste tests. The machine has three buttons labeled, "Coke," "Pepsi," and "Surprise." Whichever button is pressed, a nondescript can of soda pops out containing either Pepsi or Coke - the surprise button is supposed to randomly give a can of one or the other. Trouble is, some rascal has gone and switched the labels so now every label is wrong. Luckily, you are an expert at telling the difference between Pepsi and Coke, so if you sample one of the cans, you will be able to determine which soda it is (even though the can is no help). How many sodas must you drink to guarantee you will be able to put the labels back where they belong?


What if you discovered that the surprise button gave you a Coke?
Taste the can that you get by hitting the button with the surprise label. Without loss of generality, let's say this is a Coke. This means that this button should be labeled Coke (it cannot be the Pepsi button, because that never gives a Coke, and it cannot be the surprise button because all the labels were wrong). Now what about the other two buttons? One is labeled Pepsi, but is either the surprise or Pepsi. Since it is labeled wrong, it cannot be Pepsi, so it is the surprise button. Finally, this leaves the button labeled Coke, which must be the Pepsi button.


Richard Wiseman's Blog - new puzzle every Friday, answers on Monday.