Missing Dollar Riddle

Missing dollar riddle

The puzzle of the missing dollar is a famous puzzle that involves an informal decline. This is at least of the 1930s, though similar puzzles are very old.

Although words and nuances can change, the puzzle runs with these lines:

Three people check in a hotel room. The clerk says that the bill is $ 30, so every guest pays $ 10. Later the clerk learns that the bill should be only $ 25. To fix this, he gives the bell $ 5 to go back to the guests. On the way to the room, Belhov realizes that he can not even divide the money equally. As the guests did not know the total amount of the revised bill, Bellf decided to give only $ 1 to each guest and kept $ 2 as a tip for himself. Each guest got $ 1 back, so now every guest paid only $ 9, so that the total payment was $ 27. The Bellhouse has $ 2. And $ 27 + $ 2 = $ 29 So, if guests originally handed $ 30, what happened to the remaining $ 1? This is where the fault is. The math problem can not have two answers. It is true that for registering 25 for 25 guests and 2 = 30 for tip. However, anyway you see it, 9 × 3 = 27 + 2 = 29!

Solution

The wrong description in this puzzle is at the end of the description, where a bunch of unrelated formulas is added together, and the listener believes that these numbers should be added to 30. In fact, there is no reason to add this yoga to 30. The exact sum mentioned in the puzzle is calculated as follows:

SUM = $ 9 (Guest payment by 1) +

$ 9 (Guest pay by 2) +

$ 9 (paid by Guest 3) +

$ 2 (Money in Belf's Pocket)

The trick here is to feel that it is not the sum of money that three people have originally paid, because the clerk has to include the money ($ 25). Instead, the sum of small amount of people that can be paid by ($ 9 * 3 people = $ 27) is added, with added money that the clerk will not be required, they paid that small amount ($ 27 Payment - $ 25 actual cost = $ 2). There is another way to say this, $ 27 already includes the tip of Belafell. To add $ 2 to $ 27 it must be double-counted. So, the cost of the three guests in the room, including the tip of the bell is $ 27. Each of the 3 guests has $ 1 in the pocket, a total of $ 3 When the room's $ 27 was added to the revised cost (with tip for the bell), the total is $ 30.

To get a sum that is worth the sum of $ 30, regardless of its location, every dollar should be accounted for.

Thus, the wise yoga that we really want is this:

$ 30 = $ 1 (inside guest pocket) +

$ 1 (inside guest pocket) +

$ 1 (inside guest pocket) +

$ 2 (inside bell pocket) +

$ 25 (Hotel Cash Register)

This yoga actually comes to $ 30.

To further explain why the sum of the puzzle is not related to the actual amount, we can change the puzzle so that the discount on the room is huge. Consider the puzzle in this form:

Three people check in a hotel room. The clerk says that the bill is $ 30, so every guest pays $ 10. Later the clerk learns that the bill should be only $ 10. To fix this, he gives a $ 20 bell to return the guests. On the way to the room, Belhov realizes that he can not even divide the money equally. As the guests did not know the revised bill's total, Bellf decided to give $ 6 to each guest and kept $ 2 as a tip for himself. Each guest received $ 6 back: so now every guest paid only $ 4; A total of $ 12 paid. The Bellhouse has $ 2. And $ 12 + $ 2 = $ 14 So, if guests originally handed $ 30, what happened to the remaining $ 16?

Now it is more clear that the question is silly. No one can simply add a bunch of payments together and they can expect a basic amount of cash circulated.

More financially, in the possession of any one, wealth is calculated by adding all the paid zodiac (liabilities) together with all the money. This essence is in this posture regardless of the relative view of the actors.

Hotel guests paid $ 27, but at the end of the story there is also $ 3 between their pockets. Their property is $ 3, and their liabilities are $ 27 ($ 30 = 27 + 3), thus accounting for the original total.

From the point of view of the hotel clerk, the property lost $ 25 in the property and $ 5 in liabilities ($ 30 = 25 + 5).

From Belafell's point of view, his property is $ 2, and his liabilities are $ 3 for guests and $ 25 for registering at the desk. ($ 30 = 2 + 3 + 25).