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wonderful
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Posts: 203
 How can you meet Mr. Bin Ladden   « on: Aug 12th, 2008, 4:31pm » Quote Modify

From CIA's report you know that Bin lives in one of 13 caves. These caves can be considered as 13 points on a circle.  Everyday, Bin move to one the two  caves that are adjacent to the case he lived in the day before. Each day, you can also visit 2 caves.

What is the optimal strategy for you to find out what cave  Bin is in?

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towr
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 Re: How can you meet Mr. Bin Ladden   « Reply #1 on: Aug 13th, 2008, 1:50am » Quote Modify

Variations here and here

Here's my attempt, with 16 days:
#x#xxxxxxxxxx
#.x#xxxxxxxxx
#x.x#xxxxxxxx
#.x.x#xxxxxxx
#x.x.x#xxxxxx
#.x.x.x#xxxxx
#x.x.x.x#xxxx
#.x.x.x.x#xxx
#x.x.x.x.x#xx
#.x.x.x.x.x#x
#x.x.x.x.x.#.
#.x.x.x.x.#..
.#.x.x.x.#...
..#.x.x.#....
...#.x.#.....
....#.#......
 « Last Edit: Aug 13th, 2008, 1:51am by towr » IP Logged

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towr
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 Re: How can you meet Mr. Bin Ladden   « Reply #2 on: Aug 13th, 2008, 1:57am » Quote Modify

in 13 12 days:
xxxxx#x#xxxxx
xxxxx#.#xxxxx
xxxx#x.x#xxxx
xxx#x.x.x#xxx
xx#x.x.x.x#xx
x#x.x.x.x.x#x
#x.x.x.x.x.x#
#.x.x.x.x.x.#
.#.x.x.x.x.#.
..#.x.x.x.#..
...#.x.x.#...
....#.x.#....
.....#.#.....
 « Last Edit: Aug 14th, 2008, 12:21am by towr » IP Logged

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SMQ
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 Re: How can you meet Mr. Bin Ladden   binladden.zip « Reply #3 on: Aug 13th, 2008, 8:19am » Quote Modify

I can do you one better, based on inexorable's solution in the first thread linked above:

x#x#xxxxxxxxx
xx.x#x#xxxxxx
xxx.x.x#x#xxx
xxxx.x.x.x#x#
#x#xx.x.x.x.x
x.x#x#.x.x.x.
.x.x.x#.#.x.x
x.x.x.x..#.#.
.#.x.x.x....#
..#.#.x.x....
.....#.#.x...
........#.#..

Edit: or, more simply, just drop the top line from your diagram, towr, you don't need it.

--SMQ
 « Last Edit: Aug 13th, 2008, 9:22am by SMQ » IP Logged

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Eigenray
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 Re: How can you meet Mr. Bin Ladden   « Reply #4 on: Aug 13th, 2008, 10:47am » Quote Modify

For N caves, N>2, it can be done in N-1, if N odd;  N-2, if N even days.  Can you prove this is optimal?  (It is so for N 20.  But for N>20, it can be done in just segfault days.)
 « Last Edit: Aug 13th, 2008, 10:56am by Eigenray » IP Logged
wonderful
Full Member

Posts: 203
 Re: How can you meet Mr. Bin Ladden   « Reply #5 on: Aug 13th, 2008, 8:23pm » Quote Modify

Thanks guys! Great discussion as always.

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towr
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 Re: How can you meet Mr. Bin Ladden   « Reply #6 on: Aug 14th, 2008, 12:15am » Quote Modify

on Aug 13th, 2008, 8:19am, SMQ wrote:
 Edit: or, more simply, just drop the top line from your diagram, towr, you don't need it.
The second line, you mean. Darn, that I didn't see that before.
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