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Joined: Aug 2008
Posts: 207
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OP
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Joined: Aug 2008
Posts: 207 |
An emperor wants to marry off his daughter. The way he chooses among the suitors is this. They all sit down at a round table. The emperor walks around the table, saying to the first suitor, "You live". The second suitor is not so lucky, the emperor says "You die", and kills him on the spot with his sword. He lets the third suitor live, but the fourth dies. This goes on around the table till there's only one suitor left.
Question: Figure out where exactly to sit to be the surviving suitor, regardless of how many suitors sit at the table. Use a diagram to help you. Dh and I have tried it. DS8 has come up with his own solution too.  I believe there are more than one approach to this. (I have another solution from another boy). I would like read about yours. (Will post DS and the other boy's approach here later. )
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Joined: Sep 2008
Posts: 325
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my solution: forget the girl, get up and run! 
Last edited by ienjoysoup; 10/02/08 06:54 AM.
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Joined: May 2007
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If it's a round table, how do you know where the emperor will start? Are we to assume there is a fixed starting position?
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Joined: Jun 2008
Posts: 1,840
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Where to sit depends solely on whether the starting number of suitors is "friendly" or not, but there are only two places to sit.
I did the solution inductively.
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Joined: May 2007
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Ok, I think I figured out a formula but I can't remember how to do the little push the button and reveal thingee in my post. So I won't post it yet.
If the number of suitors is N = 2^k + n < 2^(k+1), then sit at position number 2n + 1.
Last edited by Cathy A; 10/02/08 12:06 PM. Reason: figured out UBB code
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Joined: Jun 2008
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Its a good thing he picked every 2nd suitor. With some combinations, he just goes around and around the table.
If he specifies that all the suitors must come from noble families, then he gets rid of a lot of competitors for his sons, too.
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Joined: May 2007
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Its a good thing he picked every 2nd suitor. With some combinations, he just goes around and around the table. The way I understood the problem, the emperor ignores those who are already dead and continues his elimination method on the remaining suitors.
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Joined: Aug 2008
Posts: 207
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OP
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Joined: Aug 2008
Posts: 207 |
my solution: forget the girl, get up and run! LOL!!!
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Joined: Aug 2008
Posts: 207
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OP
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Joined: Aug 2008
Posts: 207 |
If it's a round table, how do you know where the emperor will start? Are we to assume there is a fixed starting position? Yes. I think the assumption here is he always starts from the same first spot and will go round and round until he has the last remaining "living" suitor.
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Joined: Aug 2008
Posts: 207
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Hmm, your knights aren't cooperating with my table...or I'm not understanding... Are you going around the table more than once there with the 2N+1? Give me any number, and I can tell you where to sit, but I can't get a formula out of this mess! I can program a computer though, or give you a flow chart, ROFL! I have the formula. The "click to reveal" inbox is NEAT!!! I am going to try using it. 
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