Math Puzzle - Case of the Missing Dollar(?) Part 1
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Original Photo by Norsehorse Edited by Brian
There’s a braintwister that’s been going around the internet, well, probably ever since there was an internet. It’s actually probably thousands of years old in one version or another. You may have seen it phrased like this:
Three men go into a motel. The man behind the desk said that the room costs $30. So each man paid $10 and went to the room.
Later, the desk clerk realized that the room was only $25. So he sent the bellboy to the men’s rooms with five one-dollar bills.
The bellboy couldn’t figure out how to split five dollars evenly three ways, so he gave each man one dollar, and kept the other two for himself.
This meant that the three men had each paid $9 for their rooms, which makes a total of $27 dollars. Adding the two dollars that the bellboy kept would make a total of $29 dollars.
So where is the other dollar?
My advice to anyone trying to solve anything like this, or trying to think about anything at all, for that matter, is not to jump to conclusions.
Want to give it a try and add your thoughts in a comment? Go for it! I’m not asking for the solution, just some thoughts about the meaning of the puzzle - how it relates to life, logic, decision-making and understanding your world. I am not putting this up as a trivial puzzle.
My comments will be in the next post.
(Note: When I originally posted this, there were a few typos and other mistakes in it. If you busted your head over it till now, please accept my apologies. It should be correct now.)
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Comment by Karkuskwak
Haha, it’s weird that you don’t think about it right away! I’ must have stared at the screen for a good 5 mins trying to figure this out! But when you think of it, it’s simple. They give $30. They each get back 3 bucks, they’ve therefore only payed $27 total. The confusing part is that the guy gives $5 to the bellboy instead of $3. So, 9+9+9 = 27. 27+5 = 32! I felt stupid when is realised how simple it was. First time I came across it by the way.
Professor Homunculus sez:
At first glance this answer may look confusing. It was submitted as the answer to the way the question was originally worded here at the Math Mojo Chronicles. It’s a bit different from the answer to the newly worded version, above, but a similar kind of thinking will solve the new version.
By the way, there are lots of ways to look at the problem to get the correct answer.
Comment by Khaled
It took me a few minutes to wrap my head around this one. I won’t put up a solution, but I’ll say that I’m quite impressed.
This is a cool problem. It confused me simply because I began tackling it with the assumption that everything stated in the problem text was entirely accurate. Interesting how, once you assume that you can implicitly trust a given source, you can be led through any logic, or illogic, and have a lot of trouble pulling yourself back to a critical mindset.
Comment by Mark Schooley
My Dear Professor,
I started to write an equation, because properly written equations can solve all counting problems, but then realized that this was pointless, because adding 2 dollars to the 27 dollars the guests paid did not reflect what happened. They paid $27. Period. The $2 withheld by the bellboy did not constitute an additional $2 cost above the $27, it represented money refunded by the manager that didn’t get refunded to the guests. So the problem is $27 paid by the guests, MINUS the $2 “carrying charge” of the bellboy = $25 received by the motel’s manager.
Here’s a good one:
http://www.smart-kit.com/s283/.....come-from/
Hint: Don’t glibly assume something to be true from visual inspection that is not!
Comment by Laurie
My Dad loved these kinds of puzzles and I’ve known this one ever since I can remember. So, while I can’t vouch for thousands of years, I can safely say this is at least 50 years old. I’ve known the answer for nearly 50 years as well. I’ve also asked this puzzle several times.
Comment by J. Aragonesi
Great problem–took some thought. Thanks