Bürgerproteste gegen Hilberts Hotel
(Published on 10. March 2013, 14:31 by bromp)
Citizens protest against hotel plans
The publication of the call for tenders for Hilbert's Grand Hotel (see
Hilbert's Grand Hotel) caused different reactions among the citizens of Göttingen. Some were opposed to the idea of spending an infinite amount of money on a hotel, others had objections against the mathematical ideas behind the hotel plans. Among the latter a group that called itself the 'Friends of Symmetry' voiced the opinion that everything in the hotel should have at least one axis of symmetry, ideally four. Concerning the bathrooms they suggested a different layout pattern.
In addition to the other conditions (the bathrooms are suqares, the bathroom of room #N has an edge length of 2N+1 units, only square tiles, you may use tiles of sizes 1x1 to NxN, and you should use the minimum possible number of tiles) a 1x1 area in the center must not be covered with tiles.
Example: according to the Friends of Symmetry the bathroom for room #4 should look like this:
and the tiling could be done in the following way:
The tiles are marked in red. The black area in the center is the area that must not be covered by tiles. Tiles may not overlap each other, they may not be cut, and they may not extend beyond the room boundary.
As a test for any bidding tile layers the Friends of Symmetry suggest that the tiles layers should determine the first room for which the minimum required number of tiles is less than the edge length of the bathroom. Asymmetric tilings are accepted for this test.
Solution code: The solution code consists of four numbers: the room number (not the edge length of the bathroom) and the numbers of 1x1, 2x2, and 3x3 tiles that are used. For the example above the solution code would be 4, 5, 8, 3.
Solved by MiR, dm_litv, pokerke, Luigi, CHalb, r45, saskia-daniela, julius64, zorant, rimodech, flooser, Alex, ibag, pin7guin, joyal, relzzup, uvo, tuace, AnnaTh, jessica6
Comments
on 15. May 2013, 20:33 by ibag
Leicht??? Für mich jedenfalls nicht!
on 14. March 2013, 00:44 by saskia-daniela
@Julius: die Fliesen sollen kleiner als die Seitenlänge, also kleiner als 2n+1 sein. Dein n ist noch zu hoch ;-)
on 11. March 2013, 18:19 by CHalb
@Luigi: Naja, da wäre der schöne Standardlösungscode nicht eindeutig. Schwerwiegender ist aber, dass ich die gesamten Möglichkeiten noch mehr analysieren müsste. Dann vielleicht eher meine andere verdeckte Lösung mit -2.
on 11. March 2013, 16:15 by Luigi
@CHalb: Wie schon geschrieben, hatte ich genau diesen Setup schon untersucht aber gar keine Lösung mit n Fliesen bei Kantenlänge n gefunden.
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