Suppose there is a vending machine that sells Coke and Sprite. This particular vending
machine has 3 dispensers, one for Coke, one for Sprite, and the last one either dispenses Coke or Sprite at random. There's just 1 problem, all of the labels for the dispensers
have been mixed up and are incorrect! How many times do you have to buy a drink in order
to know definitely which dispenser dispenses what?
My Thinking:
Pay once: So I start at the dispenser labeled "Random." I push it and receive a Sprite. This must mean that this dispenser is for Sprite.
Pay Twice: Next, I go to the Sprite dispenser and receive a Coke. This must be the Coke dispensers.
Lastly, the last dispenser must be Random!
Does my reasoning make sense for this puzzle?
Best Answer
You needn't go to the second dispenser. Namely, once you've decided that "Random" is indeed Sprite, "Sprite" must be Coke. (Otherwise, "Sprite" would be Random, and "Coke" would be Coke, i.e. Coke wouldn't be wrongly labelled.)