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Here is the original question.

Three men go to stay at a motel, and the man at the desk charges them \$30.00 for a room. They split the cost ten dollars each. Later the manager tells the desk man that he overcharged the men, that the actual cost should have been \$25.00. The manager gives the bellboy \$5.00 and tells him to give it to the men. The bellboy, however, decides to cheat the men and pockets \$2.00, giving each of the men only one dollar.

Now each man has paid 9.00 to stay in the room and $3 \times \$9.00 = \$27.00$. The bellboy has pocketed \$2.00. $\$27.00 + \$2.00 = \$29.00$ - so where is the missing \$1.00?

( I tried to add dollar signs but this stackexchange converts those to something else (edit: just add a backslash before the dollar sign otherwise it's treated as the MathJax delimiter) ),

I found a website that answers the problem, well it provides directions so that the reader can answer for themselves. But I feel like there is a logical fallacy involved in this and I am wondering which one it is.

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  • $\begingroup$ Each man has paid \$9 for a total of \$27. Of this amount, \$25 was collected by the motel owner and \$2 by the bellboy. Put differently, the \$2 kept by the bellboy should be subtracted from the amount paid by the three men, not added to it. $\endgroup$ – Hans Engler Apr 1 '15 at 17:15
  • $\begingroup$ I don't think it has a name. It's simply confusing the sign... $\endgroup$ – Memming Apr 1 '15 at 17:16
  • $\begingroup$ Indeed, @memming , I would call it an algebra/arithmetic error $\endgroup$ – pjs36 Apr 1 '15 at 17:20
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    $\begingroup$ I'd call it bad accounting. $\endgroup$ – paw88789 Apr 1 '15 at 17:20
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    $\begingroup$ Misdirection would be my initial thought. $\endgroup$ – JB King Apr 1 '15 at 17:54
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It's not a logical error, it's an arithmetic error: adding instead of subtracting. This can be seen more clearly if the bellboy had been given \$10 to refund, but had kept \$7 for himself. The puzzle would then read "\$27 + \$7 = \$34... uh, where did the extra \$4 come from?"

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The three buddies paid $\$ 27.00\>$ in total; $\$ 25.00\>$ went to the manager, and $\$ 2.00\>$ went to the bellboy – there is no missing dollar.

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