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Topic: 2 envelopes with double money (Read 1590 times) |
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hoferman
Newbie
Posts: 10
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2 envelopes with double money
« on: Aug 17th, 2005, 5:28am » |
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I did not find anything similar to this already posted, so here we go:
There are two closed envelopes, with money inside of which you can chose one. The only thing you know is that one envelope contains double the money of the other one.
Assume you pick one, and open the envelope. There is 100 Euro inside. That means that in the other envelope there is either 50 or 200 Euro. That also means that the expected value of the other envelope is (50+200)/2 = 125 Euro. Whow, that is more than you have got in your hands. So if I ask you to swap your envelope for the other one, you should - to get more money.
Even better..
If you do not open the envelope the amount of money of the enclosed envelope in your hand is always less than the envelope I still have. This is because your amount = x ; and my amount is (2X+.5X)/2=1.25 X
Is this quantum fysics, or did something else go wrong?
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Barukh
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Posts: 2276
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Re: 2 envelopes with double money
« Reply #1 on: Aug 17th, 2005, 5:56am » |
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This puzzle has a privilege to be on the William’s List of Problems in the Hard Section under the name “ENVELOPE GAMBLE I”.
An extensive discussion may be found here.
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hoferman
Newbie
Posts: 10
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Re: 2 envelopes with double money
« Reply #2 on: Aug 17th, 2005, 5:59am » |
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on Aug 17th, 2005, 5:56am, Barukh wrote:This puzzle has a privilege to be on the William’s List of Problems in the Hard Section under the name “ENVELOPE GAMBLE I”.
An extensive discussion may be found here. |
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Thx. It is hard to determine if something was already posted when you are relatively new to this forum. Thx
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Barukh
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Re: 2 envelopes with double money
« Reply #3 on: Aug 17th, 2005, 6:16am » |
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No problem, hoferman.
You may want to try Search engine.
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JocK
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Re: 2 envelopes with double money
« Reply #4 on: Aug 17th, 2005, 11:40am » |
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on Aug 17th, 2005, 6:16am, Barukh wrote:
Sure... the problem, however, is that most of the time problems appear under 'creative titles' which are difficult to guess...
It would actually help if we would define a list of categories that can provide one or more keywords to be included (by one of the moderators?) in each of the discussion chains.
Categories could include items like: geometry, paradox, probability, combinatorics, numbertheory, ... etc. Categories could have overlap: it actually helps finding the problem you ar looking for. E.g. for the envelope paradox one could search for the two keywords 'paradox' and 'probability'.
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solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
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