11471 - Arrange the Tiles

All about problems in Volume 114. If there is a thread about your problem, please use it. If not, create one with its number in the subject.

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andmej
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11471 - Arrange the Tiles

Post by andmej » Mon Aug 04, 2008 5:49 am

I can't find a way to solve this problem other than examining all possibles boards with brute force.
How to solve this efficiently? Thanks.
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Leonid
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Re: 11471 - Arrange the Tiles

Post by Leonid » Mon Aug 04, 2008 9:35 am

Take 6 elements out of 12: (12! / (6! * 6!).
You will result in 2 groups of 6 elements. Think about what information do you need from these groups in order to find a number of ways in which the groups can be connected.

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andmej
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Re: 11471 - Arrange the Tiles

Post by andmej » Wed Aug 06, 2008 3:39 pm

I still haven't found the solution. Any other hint?
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Robert Gerbicz
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Re: 11471 - Arrange the Tiles

Post by Robert Gerbicz » Wed Aug 06, 2008 7:03 pm

Code: Select all

aaa
aaa
bbb
bbb

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andmej
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Re: 11471 - Arrange the Tiles

Post by andmej » Sun Aug 10, 2008 12:33 am

Robert Gerbicz wrote:

Code: Select all

aaa
aaa
bbb
bbb
I think that once I have split the tiles in two groups of 6, I have various ways (4!) to order rows of 3 tiles taken from the two groups, including:

Code: Select all

A1
A2
B1
B2
and

Code: Select all

A2
B1
B2
A1
etcetera.

But if I check all of these arrangements there might be some that are legal but not counted. What to do?
Runtime errors in Pascal are reported as Wrong Answers by the online judge. Be careful.

Are you dreaming right now?
http://www.dreamviews.com

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rio
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Re: 11471 - Arrange the Tiles

Post by rio » Tue Aug 12, 2008 10:33 am

You could also get AC using simple Backtrack with a little trick.

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Rio

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