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        riddles >> medium >> 2 envelopes with double money
        
(Message started by: hoferman on Aug 17^th, 2005, 5:28am)

Title: 2 envelopes with double money
Post by hoferman on Aug 17^th, 2005, 5:28am

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?

Title: Re: 2 envelopes with double money
Post by Barukh on Aug 17^th, 2005, 5:56am

This puzzle has a privilege to be on the William’s List of Problems in the Hard Section (http://www.ocf.berkeley.edu/~wwu/riddles/hard.shtml) under the name “ENVELOPE GAMBLE I”.

An extensive discussion may be found here (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_hard;action=display;num=1027910317;start=0).

Title: Re: 2 envelopes with double money
Post by hoferman on Aug 17^th, 2005, 5:59am

on 08/17/05 at 05:56:10, Barukh wrote:

Thx. It is hard to determine if something was already posted when you are relatively new to this forum. Thx

Title: Re: 2 envelopes with double money
Post by Barukh on Aug 17^th, 2005, 6:16am

No problem, hoferman.

You may want to try Search engine (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=search).

Title: Re: 2 envelopes with double money
Post by JocK on Aug 17^th, 2005, 11:40am

on 08/17/05 at 06:16:37, Barukh wrote:

You may want to try Search engine (http://www.ocf.berkeley.edu/~wwu/cgi-bin/yabb/YaBB.cgi?board=riddles_medium;action=search).

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'.