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Post by Galvin on May 11, 2008 23:42:14 GMT -7
Ok, here's one to put in yer dog dish and sniff.
Picture a REALLY cheap hotel.
Now picture three guys who are even cheaper than the hotel because they stagger in drunk early one morning to sleep it off and decide to save money by sharing one room.
The night clerk charges them $30.00 for the room and they each kick in ten bucks.
But when the manager shows up the next day and sees what the night clerk has charged the three guys he is a little put off that the night clerk doesn't know that he only charges the hookers $25.00 for that room and everyone gets the same price whether they are working or not. So he sends the bellhop over with a $5.00 refund.
On the way to the room the bellhop rationalizes to himself that dividing $5.00 three ways will be too inconvenient. So he pockets $2.00 of the five and gives each of the three occupants $1.00 each from the remaining three bucks.
With me so far?
Each of the three men has therefore paid $9.00 ($10.00 minus the $1.00 refund) or a total for all three of $27.00. That $27.00 added to the $2.00 the bellhop snagged gives us a grand total of $29.00.
But they originally paid $30.00.
So what happened to the missing buck?
(It is alleged that only three percent of the people who attempt to do this problem can figure it out correctly and of those who do so successfully, more are women than men).
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Post by Patch on May 12, 2008 17:53:32 GMT -7
23 views and no takers yet?
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Post by zrct02 on May 14, 2008 21:55:40 GMT -7
Here's a try.
The error arises from rounding.
They each got $1 = $3 and each *tipped* the bellhop $2/3 = $2.
They didn't know they actually paid $8 1/3 for the room = $25.
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Post by invisible on May 29, 2008 14:11:11 GMT -7
You are missing three bucks, not one.
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Post by zrct02 on May 30, 2008 13:15:57 GMT -7
Uh?
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Post by invisible on May 30, 2008 13:32:26 GMT -7
$27 + $3 + $2 = $32: The actual cost of the room was $9 each + $1 each from the owner.
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Post by zrct02 on May 30, 2008 18:48:28 GMT -7
Errors arise from using the owner's perspective and/or the clients' perspective. None of them knows what the bellhop did.
We do.
We know they paid $25 for the room.
We know they got $3 total refund
We know the bellhop kept $2
The $27 includes the $3 they each got back, so including it counts that $3 twice.
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Post by invisible on Jun 5, 2008 7:26:03 GMT -7
No, they originally paid $30 for the room, and the bellhop gave each back one dollar. The three dollars he gave back was their three dollars originally. So there is no reason that $27 + $2 should add up to $30. The $2 is outside the transaction between the renters and the bellhop. Or: $30 - $3 + $2 = $29
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Post by zrct02 on Jun 5, 2008 8:30:10 GMT -7
They originally paid $30 - $10 each. The proprietor reduced that to $25. That's $8.33 each (rounded). Each was to get back $1.66 each.
They got back $1.00 each which meant they effectively paid $9.33 each - not $9.00. That's $28/3. The $2 the bellhop kept is part of the transaction, but was unknown to the proprietor and the guests.
The proprietor got $25 or $8.33 (rounded) each.
The guests got back $3.00 or $1.00 each
The bellhop got $2.00
$25 + $3 + 2 = $30
To account for all the money, one cannot look at it from the perspective of the guests as they do not know all of the exchanges involved.
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Post by invisible on Jun 5, 2008 10:34:05 GMT -7
No, again. They paid $30 for the room. The owner tried to reduce the price to $25, but was unsuccessful, because the bellhop kept $2 out of the deal. So the price was reduced to $27, i.e. $9 each, not $25 total. T,he owner thinks they paid $25, but they paid $27 and the bellhop hopes they do not discuss the matter with the owner.  |
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Post by zrct02 on Jun 5, 2008 17:34:53 GMT -7
They paid a total of $28 including the bellhop's take. $30 - $2 = $28. That's $9.33 each.
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Post by invisible on Jun 6, 2008 7:26:33 GMT -7
I give up.  |
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Post by zrct02 on Jun 6, 2008 11:52:08 GMT -7
Last chance. assume the original price was $36 ($12 each) assume the owner reduced it to $30 bellhop gave back only $3 instead of $6 renters think they paid $33 for room ($12 - $1) = $11 X 3 = $33 bellhop kept $3 bellhop's $3 + renter's $33 = $36 Exactly same situation but with no rounding errors, the numbers come out correct. |
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Post by invisible on Jun 6, 2008 16:12:39 GMT -7
There are no rounding errors in the original situation, because the bellhop avoided them. Just the misstatement that $27 + $2 should = $30
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Post by zrct02 on Jun 6, 2008 18:23:44 GMT -7
The Bellhop only avoided the rounding at the end of the transaction. He couldn't avoid the rounding at the beginning. Therefore, the $27 is a fiction.
In my example, there is no rounding so the numbers come out right.
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Post by jetmex on Jun 14, 2008 13:00:28 GMT -7
Not hard to figure out..the lost buck was the taxes. No one ever seems to know where they go..... ;D
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Post by waynec on Nov 9, 2008 21:28:39 GMT -7
They paid $30. They were refunded three. 30-3=27. The two the bell hop kept was not part of the purchase. It was part of the refund. 30-3=27. 27-2=25. To say that 27+2=29 takes the bell hops two in the wrong direction. He isn't adding. He is subtracting. 27 they paid after the refund minus two that the bell hop kept results in 25 that they were charged. Or, 25 that they were charged plus the 3 that they were refunded comes to 28. 28 plus the 2 that the bell hop kept comes to 30. 9x3=27 is an interesting mathematical fact but has nothing to do with the actual direction that the funds traveled.
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