Related: Trust in Math

I was reading John Allen Paulos' A Mathematician Plays the Stock Market, in which Paulos relates a version of the well-known "missing dollar" riddle. I had heard it once before, but only vaguely remembered it. If you don't remember it, here it is:

Three people stay in a hotel overnight. The innkeeper tells them that the price for three rooms is $30, so each pays $10.
After the guests go to their rooms, the innkeeper realizes that there is a special discount for groups, and that the guests' total should have only been $25.
The innkeeper gives a bellhop $5 with the instructions to return it to the guests.
The bellhop, not wanting to get change, gives each guest $1 and keeps $2.
Later, the bellhop thinks "Wait - something isn't right. Each guest paid $10. I gave them each back $1, so they each paid $9. $9 times 3 is $27. I kept $2. $27 + $2 is $29. Where did the missing dollar go?"

I remembered that the solution involves trickery, but it still took me a minute or two to figure out where it is. At first, I started mentally keeping track of the dollars in the riddle, trying to see where one got dropped so their sum would be 30.

Then I figured it out. The story should end:

Later, the bellhop thinks "Wait - something isn't right. Each guest paid $10. I gave them each back $1, so they each paid $9. $9 times 3 is $27. The cost for their rooms was $25. $27 - $25 = $2, so they collectively overpaid by $2, which is the amount I kept. Why am I such a jerk?"

I told my fiance the riddle, and asked her where the missing dollar went. She went through the same process as I did, looking for a place in the story where $1 could go missing.

It's remarkable to me how blatantly deceptive the riddle is. The riddler states or implies at the end of the story that the dollars paid by the guests and the dollars kept by the bellhop should be summed, and that that sum should be $30. In fact, there's no reason to sum the dollars paid by the guests and the dollars kept by the bellhop, and no reason for any accounting we do to end up with $30.

The contrasts somewhat with the various proofs that 1 = 2, in which the misstep is hidden somewhere within a chain of reasoning, not boldly announced at the end of the narrative.

Both Paulos and Wikipedia give examples with different numbers that make the deception in the missing dollar riddle more obvious (and less effective). In the...

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