the lost dollar puzzle is a well-known puzzle that involves an informal fallacy. It dates back to at least the 1930s, although similar puzzles are much older.
Although the words and specifications may change, the puzzle goes along these lines:
Three people checked the hotel room. The clerk said his bill was $ 30, so each guest paid $ 10. Then the clerk realized the bill only had to be $ 25. To fix this, she gave the $ 5 bellhop to get back to the guests. On the way to the room, the bellboy realizes that he can not even divide his money evenly. Since the guests did not know the total amount of the revised bill, the bellhop decided to just give each guest $ 1 and save $ 2 as a tip for himself. Every guest gets $ 1 back, so now every guest only pays $ 9, so the total becomes $ 27. Bellboy has $ 2. And $ 27 $ 2 = $ 29 So if the guest initially handed over $ 30, what happened to $ 1 the remaining?
Video Missing dollar riddle
Solution
The error in this puzzle is at the end of the description, where a bunch of unrelated numbers are added together, and the listener assumes these numbers should add 30. Actually, there is no reason this number should be added to 30. The exact amount mentioned in the puzzle is calculated as:
The trick here is to realize that this is not the amount of money paid by the three people, because it needs to put in the money the officer has ($ 25). This is not a smaller amount that people can pay ($ 9 * 3 people = $ 27), plus extra money that unnecessary workers require if they pay a smaller amount ($ 27 paid - $ 25 actual fee = $ 2). Another way to say this is, $ 27 already includes a tip of the waiter. To add $ 2 to $ 27 will be doubled. So, the cost of three guest rooms, including the tip of the maid, was $ 27. Each of the 3 guests had $ 1 in his pocket, for $ 3. When added to the revised $ 27 room fee (including tip to bellboy), the total was $ 30.
To get the original total up to $ 30, every dollar must be accounted for, regardless of location.
So, the reasonable amount we want is this one:
This amount does reach $ 30.
To illustrate further why the number of puzzles is not related to the actual number, we can change the puzzle so that the discount on the room is very large. Consider the puzzle in this form:
Three people checked the hotel room. The clerk said his bill was $ 30, so every guest paid $ 10. Then the clerk realized the bill only had to be $ 10. To fix this, he gave the $ 20 bellhop to get back to the guests. On the way to the room, the bellboy realizes that he can not even divide his money evenly. Since the guests did not know the total amount of the revised bill, the bellhop decided to just give each guest $ 6 and save $ 2 as a tip for himself. Every guest gets $ 6 back: so now every guest pays only $ 4; bring the total paid to $ 12. Bellboy has $ 2. And $ 12 $ 2 = $ 14 so, if the guest initially handed over $ 30, what happened to the remaining $ 16?
Now it is clear that the question is ridiculous. People can not just add a lot of payments together and expect them to total the amount of cash in circulation.
More economically, money is accounted for by adding up all the amount paid (liabilities) with all the money in a person's (asset) holdings. The abstract formula applies regardless of the relative perspective of principals in this exchange.
- The hotel guests pay $ 27, but also have $ 3 between their pockets at the end of the story. Their assets are $ 3, and their liabilities are $ 27 ($ 30 = 27 3) Thus the original totals are recorded.
- From the perspective of hotel clerk, the hotel has $ 25 in assets and lost $ 5 in liabilities ($ 30 = 25 5).
- From a bellhop's perspective, the asset is $ 2, and the obligation is $ 3 for guests and $ 25 to sign up at the table. ($ 30 = 2 3 25).
Maps Missing dollar riddle
History
There are many variants of the puzzle. Professor David Singmaster
A misdirection in 1880 was given as "Barthel saw two boxes in a jewelry store, for a price of 100 and 200. He bought a cheaper one and brought it home, where he decided he really preferred the other." He returned to the jewelry store and give him the box back and say that the jewelry already has 100 of it, which along with the box returned, earns 200, which is the cost of the other box.Jewelry accepts this and gives Barthel another box and Barthel continues his journey.
A more similar model in style to the modern version is given by Cecil B. Read in 1933 Mathematical error. The puzzle generates extra dollars. A man put $ 50 in the bank. Then in the following days he pulled $ 20 and left $ 30; then withdraw $ 15 leaving $ 15; draw $ 9 to $ 6; pulling $ 6 leaving $ 0. But $ 30 $ 15 $ 6 = $ 51. Where does that extra dollar come from?
The real solution to this puzzle is to add it correctly (the right time, the right person and the correct location) from the viewpoint of the bank which in this case seems to be the problem: 1) The first day: 30 $ in the bank 20 $ the owner is already attractive = 50 $ 2) Second day: 15 $ in bank (15 $ 20 $ owner already resigned) = 50 $ 3) Third day: 6 $ in bank (9 $ 15 $ 20 $ owner already withdraw) = 50 $
From the owner point of view the correct solution is this: 1) First day: 20 $ owner already resigned 30 $ at bank = 50 $ 2) Second day: 20 $ owner already resigned 15 $ owner already resigned 15 $ at bank = 50 $ 3) Third day: (20 $ owner already resigned 15 $ owner already withdraw 9 $ owner already resigned) 6 $ at bank = $ 50
The solution seems very clear if the owner pulls each day only 10 $ from $ 50. To add 40 30 20 10 using the same pattern from above will be too obviously wrong (the result is $ 100).
The answer to the question: ,, Where did the extra dollars come from? "From successively adding a bank break from three different days.This is true only if the money owner pulls out every day exactly half of the money.Through it will add up. (25 $ 12.5 $ 6.25 $) 6, 25 $ = 50 $
Another entry from 1933, R. M. Abraham Redirects and the Past (still available in Dover version) has a slightly different approach to this problem from page 16 (problem 61). "A sic who returned to New York discovered that he only had ten dollars' worth of money, and that the train cost was seven dollars.The ticket officer refused to accept the money order, so the traveler crossed the road to mortgage the pawn and pawned it for seven dollars On the way back to the station, he meets a friend, who, in order to save the traveler, trouble redeeming the money order, buy his seven-dollar pledge ticket, buy his ticket and still have seven dollars when he gets to New York. loss? "David Darling in his book The Universal Mathematical Book , considers this as an earlier version of three people in the hotel version above.
Even more like the English, The Black-Out Book by Evelyn August in 1939; What happened to shilling ?, pp. 82 & amp; 213. Three girls each paid five shillings to share a room. The owner returned the money 5 shillings through the bellboy, who gave them each and saved two.
And another one of the same themes appears in the regular Abbott and Costello where Abbot asks Costello for a fifty-dollar loan. Costello holds forty dollars and says, "That's all I have." Abbas replied, "Well, you can owe me ten others."
This puzzle is used by psychotherapist (Chris Langham) with his mathematician client (Paul Whitehouse) in episode 5 of the 2005 BBC comedy series Help ,
See also
- Missing the square riddle
References
External links
- Snopes page: "Missing Dollar Puzzle"
- Today's Psychology: "Where's the Lost Dollar?"
Source of the article : Wikipedia
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