Author Topic: One dollar puzzle  (Read 122 times)

Cas

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One dollar puzzle
« on: March 16, 2020, 08:41:39 AM »
You probably know some variation of this one. I know it like this:

- Three friends are travelling in a car on a long road and there hasn't been anything on it for hundreds of kilometers. They're tired and want some rest. They finally spot a small hostel or something like it. They stop by, get off the car and talk to a man at the entrance.
- The man says he's not the owner, that he'll be coming in an hour or so. When the friends ask for rooms, the man says he only has one left. He doesn't know the exact rate, but if the friends want to share it, he'll charge them $30 and they can go and sleep. When they wake up, he'll let them know if there's a difference, but won't be much for sure. So the friends take the room and each pays $10, totalling $30.
- When the owner arrives, the three friends are still asleep. The owner's replacement tells him about the rented room and that he's charged $30 for it. The owner says "You've charged them too much. It's actually $25 for that room. When the kids wake up, give them $5 back". But the guy thinks "How will I give $5 to three people?  Better just keep $2 for myself and give $1 back to each of them". And thus he does.
- Now the problem is this: if each one had paid $10 and is now given $1 back, then each actually paid $9. But they are three, so this is 3 times $9, which makes $27... plus the $2 that the guy kept, that's $29. So where is the other dollar?

RECOMMENDATION: If you see that somebody's posted an answer. First think about the puzzle before reading the replies. When I've given this problem to several people together, they tend to quickly influence one another and that's less interesting, even if they're wrong!

AND NOTE: People tend to stop for a moment and then tell me something like "You're saying it wrong" and then, they proceed to explain everything again just like I said it from the beginning. I know it happened that way. My question is precisely, how come if it happened that way, then it turns out a dollar is missing when we make the count?
« Last Edit: March 16, 2020, 08:46:18 AM by Cas »
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Usrin

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Re: One dollar puzzle
« Reply #1 on: March 16, 2020, 01:34:58 PM »
But they are three, so this is 3 times $9, which makes $27... plus the $2 that the guy kept, that's $29.

Why plus? The $2 the guy kept is PART of the $27 they payed, so the count in the puzzle was wrong at this point. The remaining $3 is what they got back. $27+$3=$30, and there is no missing dollar.
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Overdrijf

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Re: One dollar puzzle
« Reply #2 on: March 16, 2020, 10:14:11 PM »
27-2=25, which is the rate of the room, and 2+3=5, which is the money the owner returned.

Cas

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Re: One dollar puzzle
« Reply #3 on: March 18, 2020, 06:32:18 AM »
I guess it's much clearer in writing, ha, ha. In spoken, everybody ends up pretty confused! XD
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