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Alphabetize my Dvd's


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#1 BMAD

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Posted 20 July 2013 - 05:43 AM

My DVD Shelves used to be organized by genre and frequency of watching.  Now that I spend less time watching DVDs I find myself desiring to arrange these DVDs in alphabetical order.  I don't care if they are left to right OR right to left, i am not that picky.  To arrange my DVDs with precision I will take one DVD off the shelf and place it in the correct spot back on the shelf.  If I have 11 DVDs what is the most moves I can expect to make?  What if I had two shelves of 11 DVDs each?


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#2 TimeSpaceLightForce

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Posted 21 July 2013 - 02:21 PM

Spoiler for sloted


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#3 gavinksong

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Posted 21 July 2013 - 03:05 PM

BMAD, you are an extremely prolific topic-starter. Where do you get all these puzzles? Just to make sure I'm getting this right: You are rearranging the shelf by repeatedly taking a DVD and moving to a new spot on the shelf, and we assume that you will always rearrange the shelf in the most efficient way possible (fewest number of moves) and that you will order them left-to-right or right-to-left depending on which is faster. The problem is to find the initial order of DVDs that will result in the most number of moves. Am I right? :S Also, in the two shelf problem, is it the same as just arranging 22 DVDs on a single shelf, arranging 11 DVDs on a single shelf twice, or arranging 22 DVDs on two shelves at once except the top shelf can go left-to-right while the bottom can go right-to-left?
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#4 gavinksong

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Posted 21 July 2013 - 03:39 PM

Spoiler for

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#5 BMAD

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Posted 21 July 2013 - 05:24 PM

BMAD, you are an extremely prolific topic-starter. Where do you get all these puzzles?

Just to make sure I'm getting this right:
You are rearranging the shelf by repeatedly taking a DVD and moving to a new spot on the shelf, and we assume that you will always rearrange the shelf in the most efficient way possible (fewest number of moves) and that you will order them left-to-right or right-to-left depending on which is faster. The problem is to find the initial order of DVDs that will result in the most number of moves.

Am I right? :S

Also, in the two shelf problem, is it the same as just arranging 22 DVDs on a single shelf, arranging 11 DVDs on a single shelf twice, or arranging 22 DVDs on two shelves at once except the top shelf can go left-to-right while the bottom can go right-to-left?


Some of the problems are familiar questions twisted enough to challenge thinking, others are 'classics' that I don't find on here, and lastly some more come from the mundane. Surprisingly the mundane produce some of my favorite problems (tying spaghetti noodles, arranging DVDs, etc. ). I hope I am using mundane correctly, as in problems derived from reali life situations.

Your analysis to the first question is correct. We now have 22 DVDs and two shelves to arrange them on each holding a maximum of 11 DVDs. Work the problem out in a few cases and you will see if it is the same as 22 DVDs on one shelf or not.
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#6 BMAD

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Posted 21 July 2013 - 05:24 PM

Thank you for the praise btw
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#7 BMAD

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Posted 21 July 2013 - 05:33 PM

Spoiler for


I wonder if you could arrange 11 DVD titles say A, B, C, D, E, F, G, H, I, J, K are the titles to produce 9 moves
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#8 BMAD

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Posted 21 July 2013 - 11:42 PM

For example, suppose this is the current arrangement:
BDFHJACEGIK
Moves:
1. ABDFHJCEGIK (move A)
2. ABCDFHJEGIK (move C)
3. ABCDEFHJGIK (move E)
4. ABCDEFGHJIK (move G)
5. ABCDEFGHIJK (move I)
So only 5 moves until they are in order.
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#9 gavinksong

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Posted 22 July 2013 - 02:04 AM

 

Spoiler for


I wonder if you could arrange 11 DVD titles say A, B, C, D, E, F, G, H, I, J, K are the titles to produce 9 moves

 

 

Trying to do this makes me think that the true answer may be much lower than my generous upper bound. I can't even do it for 5 DVDs (3 moves). This problem seems to be much more complicated than it looks at first glance.  :wacko:

Especially when you extend it to two shelves. I assume that you can temporarily have more than 11 DVDs on one shelf (theoretically), but there must be 11 DVDs on each shelf at the end. Since adding a DVD to one shelf won't push the last DVD over onto the next shelf, you must move that DVD over manually if it needs to be on the other shelf - so it's definitely not the same as 22 DVDs on one shelf. There's also the issue of whether each shelf can independently go right-to-left or left-to-right regardless of how the other shelf was sorted. If that's the case, then the problem becomes even more complicated.

 

Great original puzzle, BMAD. I'm impressed.  :thumbsup: But I'm afraid that it may be above my skill level.


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#10 BMAD

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Posted 22 July 2013 - 05:11 AM

I have faith in you. But yes, either shelf can go left to right or right to left and must end with 11 DVDs
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