Last night, my wife and I were talking about math logic problems. Just wait - we really do talk about a lot more than mathematics. My wife happens to be a middle school math and algebra teacher, and she was trying to find some math puzzles or logic problems to include as bonus questions on her students' next homework assignment. She was testing the problems on me - I think she figures that if I figure out the right answer then her students probably will be able to as well (and she is absolutely, positively, 100% correct for doing so - math was never my strongest subject). Well, she found one. And I gave up on it after about 5 minutes. Apparently it is a well-known problem called the "missing dollar riddle" and it goes like this:
Three people check into a hotel room. The clerk says the bill is $30, so each guest pays $10. Later, the clerk realizes the bill should only be $25. To rectify this, she gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guest didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $2 as a tip for himself.
Each guest got $1 back, so now each guest only paid $9, bringing the total paid to $27. The bellhop has $2. And $27 + $2 = $29 so, if the guests originally handed over $30, what happened to the remaining $1?
Figure it out yet? I told my wife (with the usual, "why do you ask me to do these, I hate math brain teasers!") that the answer was impossible, "$30 is $30!" After giving up on any help from me, my wife did what she always does in these cases - she text messaged my four children to see what they thought! The two oldest never responded (SMART!!). The youngest responded with a "That a-hole bellhop clearly stole the last $1!" And, the other one apparently had heard the problem before and forwarded the link to the answer on the Internet.
The answer really is simple - and, after you look at the answer (see the Wikipedia page here) you will realize that I was absolutely correct (for once). It's a trick question - the $9 paid by each guest is already included in the original $25 that the hotel clerk now holds in her cash register. The breakdown of the actual money changing hands goes like this:
$25 - for the room (now with the hotel clerk at the front desk)
$3 - refund to the three hotel guests (3 x $1)
$2 - "tip" that the bellhop kept for himself.
Now do you understand it? As with many logic problems, the trick to figuring out the puzzle is to not make assumptions. The trick here is to think through the problem in an organized, logical fashion - using pictures (or even real dollar bills) also helps! But don't overthink it - you will end up going in circles. Don't ever assume that the simplest explanation (in this case, the fact that $27 + $2 does not equal $30) is the correct one. Never assume anything.
I think this is a great example of the high reliability organization principle of reluctance to simplify. Quick logic ($27 + $2 = $29, not $30) doesn't get you to the right answer. Only by thinking through the problem in a logical fashion (the clerk has $25, the guests have $3, and the bellhop has $2) will get you to the answer to the riddle.
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