Each guest got $6 back: so now each guest only paid $4 bringing the total paid to $12. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $6 and keep $2 as a tip for himself. On the way to the room, the bellhop realizes that he cannot divide the money equally. To rectify this, he gives the bellhop $20 to return to the guests. Later the clerk realizes the bill should only be $10. The clerk says the bill is $30, so each guest pays $10. To further illustrate why the riddle's sum does not relate to the actual sum, the riddle can be altered so that the discount on the room is extremely large. Thus, the sensible sum can be expressed in this manner: To obtain a sum that totals to the original $30, every dollar must be accounted for, regardless of its location. When added to the $27 revised cost of the room (including tip to the bellhop), the total is $30. Each of the 3 guests has $1 in his pocket, totaling $3. So, the three guests' cost of the room, including the bellhop's tip, is $27. To add the $2 to the $27 would be to double-count it. Another way to say this is, the $27 already includes the bellhop's tip. This is instead a sum of a smaller amount the people could have paid ($9 × 3 people = $27), added with the additional money that the clerk would not have needed had they paid that smaller amount ($27 paid - $25 actual cost = $2). The trick here is to realize that this is not a sum of the money that the three people paid originally, as that would need to include the money the clerk has ($25). The exact sum mentioned in the riddle is computed as: The misdirection in this riddle is in the second half of the description, where unrelated amounts are added together and the person to whom the riddle is posed assumes those amounts should add up to 30, and is then surprised when they do not - there is, in fact, no reason why the (10 − 1) × 3 + 2 = 29 sum should add up to 30. On the one hand it is true that the $25 in the register, the $3 returned to the guests, and the $2 kept by the bellhop add up to $30, but on the other hand, the $27 paid by the guests and the $2 kept by the bellhop add up to only $29. There seems to be a discrepancy, as there cannot be two answers ($29 and $30) to the math problem. So if the guests originally handed over $30, what happened to the remaining $1? The bellhop kept $2, which when added to the $27, comes to $29. As the guests are not aware of the total of the revised bill, the bellhop decides to just give each guest $1 back and keep $2 as a tip for himself, and proceeds to do so.Īs each guest got $1 back, each guest only paid $9, bringing the total paid to $27. On the way to the guests' room to refund the money, the bellhop realizes that he cannot equally divide the five one-dollar bills among the three guests. To rectify this, he gives the bellhop $5 as five one-dollar bills to return to the guests. Later the manager realizes the bill should only have been $25. The manager says the bill is $30, so each guest pays $10. Statement Īlthough the wording and specifics can vary, the puzzle runs along these lines: It dates to at least the 1930s, although similar puzzles are much older. The missing dollar riddle is a famous riddle that involves an informal fallacy. Riddle involving informal fallacy in money
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