The drinks machine with every button wrong

Question

A vending machine has three buttons labelled Tea, Coffee and Random (random gives tea or coffee unpredictably). The machine has been wired wrongly so that every button does something other than what its label says. Each press costs 50p and delivers one drink.

What is the smallest amount of money you must spend to determine, with certainty, what every button actually does?

Accepted Answer

50p: press the button labelled "Random" once. Why that button. Every label is wrong, so the button marked Random is not random: it is the tea button or the coffee button. Pressing it once tells you which. Finishing the deduction. Suppose it gives tea, so the button marked Random is really Tea. The remaining roles, Coffee and Random, belong to the buttons marked Tea and Coffee. The button marked Coffee cannot be Coffee, so it must be Random, and the button marked Tea must then be Coffee. (If the first press had given coffee, the same reasoning gives: marked Random is Coffee, marked Tea is Rand…

The drinks machine with every button wrong

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