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Topic: 100 paintings (Read 3054 times) |
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spanchap
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Suresh
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100 paintings
« on: Mar 22nd, 2007, 10:30pm » |
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There are 100 sculptures stored in 100 rooms. The scupltures are stored randomly - the best sculpture could be in any one of the 100 rooms.
You get to evaluate the sculptures beginning from room # 1 and walking thru successive rooms till you reach room #100. You are an expert in evaluating sculptures and are able to determine the relative rank of all sculptures in rooms 1 thru n when you have visited the first n rooms. Also, you know that no two sculptures have the same rank.
When you visit any given room , say room # p, you can declare that the sculpture in room p is the best sculpture among the 100 sculptures.
Once you have moved past a room, you do not get credit for declaring the sculpture in that room to be the best even though you might reach that conclusion after visiting the subsequent rooms.
What is your strategy to find the best sculpture if you get only one chance to go thru the 100 rooms?
What is your strategy to find the best sculpture if you get to do this exercise many times (say at different museums with different set of sculptures)?
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towr
wu::riddles Moderator
Uberpuzzler
Some people are average, some are just mean.
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Re: 100 paintings
« Reply #1 on: Mar 23rd, 2007, 2:13am » |
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This problem is also on the site as "bachelor dilemma", I think. And possible under a few other guises.
The result is well-known enough; proving it (at least for general N, rather than just 100) is quite a task though, if memory serves me right.
We've also considered the case were you know the distribution of value in one thread.
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| « Last Edit: Mar 23rd, 2007, 2:24am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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spanchap
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Suresh
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Re: 100 paintings
« Reply #2 on: Mar 23rd, 2007, 7:23am » |
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Thanks for letting me know that this puzzle has already been discussed. I will check that out. BTW, the solution is deceptively simple.
-Suresh
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Whiskey Tango Foxtrot
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Sorry Goose, it's time to buzz a tower.
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Re: 100 paintings
« Reply #3 on: Mar 23rd, 2007, 7:56am » |
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Here's a link in case the search function proves too fickle.
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"I do not feel obliged to believe that the same God who has endowed us with sense, reason, and intellect has intended us to forgo their use." - Galileo Galilei
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SWF
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Re: 100 paintings
« Reply #5 on: Mar 23rd, 2007, 6:21pm » |
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Why is the subject of this "100 paintings" when there are 100 sculptures?
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spanchap
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Suresh
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Re: 100 paintings
« Reply #6 on: Mar 23rd, 2007, 6:52pm » |
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My bad. Should have been 100 sculptures.
I guess I was unconsciously giving somebody an opportunity to correct me. Now I wonder what that says about me...
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