0

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?

Natalie Clarius
  • 10,530
  • Assuming all labels are now incorrect (and haven't just been randomly mixed up) then going for the dispenser labelled "Random" first seems like a good strategy. But how do you know the second dispenser is not the "Random" one? – PeteBabe Sep 05 '20 at 18:45
  • Okay, I see your point. What if I start at the "Random" one and bought a drink and it was Sprite, then this has to be Sprite. At the "Sprite" one I should buy two drinks to see if it random? Is that where I should be headed? –  Sep 05 '20 at 18:48

1 Answers1

1

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.)