When you get to the last bit, it should read: The women paid 3 X 9000 each that is 27000, the bell-hop kept 2000, and the hotel had 25000. 25000 plus 2000 is 27000.
The key statement in that explanation is probably this:
There is no reason to add the $2 and $27 – the $2 is contained within the $27 already. Thus the addition is meaningless. Instead the $2 should be subtracted from the $27 to get the revised bill of $25.
The rest, as they say, is misdirection. Last section (cash flow analysis) summarizes the various transactions quite nicely.
1) The women come to the hotel with 10k yen each; the hotel and the bellhop currently have (out of the money being passed around) 0 yen.
2) Three women each pay 10k yen to the hotel; hotel now has 30k yen, the women and the bellhop have 0.
3) Hotel gives 5k to the bellhop to return to the women; the hotel now has 25k, the bellhop has 5k, and the women 0 each.
4) The bellhop gives 3k yen to the women and keeps 2k; the women now have 1k each, the bellhop has 2k, and the hotel 25k. Each of the women has effectively paid 9k yen for the room, but not to the hotel; they've each paid 8 1/3 k to the hotel and 2/3 k to the bellhop, and gotten 1k of their original payment back.
When you look at in terms of keeping track of where each bit of money goes at each state, the confusion clears up.
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When you get to the last bit, it should read:
The women paid 3 X 9000 each that is 27000, the bell-hop kept 2000, and the hotel had 25000. 25000 plus 2000 is 27000.
It still throws me every time I read a variation
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And the end:
The hotel has 25,000.
The women have 3,000.
The bellhop has 2,000.
Which equals: 30,000.
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There is no reason to add the $2 and $27 – the $2 is contained within the $27 already. Thus the addition is meaningless. Instead the $2 should be subtracted from the $27 to get the revised bill of $25.
The rest, as they say, is misdirection. Last section (cash flow analysis) summarizes the various transactions quite nicely.
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1) The women come to the hotel with 10k yen each; the hotel and the bellhop currently have (out of the money being passed around) 0 yen.
2) Three women each pay 10k yen to the hotel; hotel now has 30k yen, the women and the bellhop have 0.
3) Hotel gives 5k to the bellhop to return to the women; the hotel now has 25k, the bellhop has 5k, and the women 0 each.
4) The bellhop gives 3k yen to the women and keeps 2k; the women now have 1k each, the bellhop has 2k, and the hotel 25k. Each of the women has effectively paid 9k yen for the room, but not to the hotel; they've each paid 8 1/3 k to the hotel and 2/3 k to the bellhop, and gotten 1k of their original payment back.
When you look at in terms of keeping track of where each bit of money goes at each state, the confusion clears up.
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