CFF Contest 28 Torsten Sillke
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Crossless L-Tromino Rectangles
Many different rectangles can be formed with identical L-trominoes. In this
contest we look for a specific type, for rectangles where no crossing occur
at the interfaces of the pieces. Figure 1 shows an L-tromino, an illegal
crossing and as an example, a crossless 5*9 rectangle.
+---+
| |
+---+---+ L-tromino
| | |
+---+---+
+---+
| |
+---+---+ +---+
| | |
+ +---X---+---+ A crossing
| | | |
+---+ + +---+
| | |
+---+---+---+
+---+---+---+---+---+---+---+---+---+
| | | | | |
+ +---+ +---+ +---+ +---+ + a crossless 5*9 rectangle
| | | | | | | | |
+---+ +---+ +---+---+---+ +---+
| | | | | |
+---+---+ +---+---+ +---+---+---+
| | | | | | | |
+ +---+---+ + +---+ +---+ +
| | | | | |
+---+---+---+---+---+---+---+---+---+
In this contest three questions should be answerd.
1. For which values of n can you find infinite series of crossless
rectanggles.
2. How many and which separate crossless rectangles can you find?
3. For which values (and series) are no crossless rectangles?
Please submit your answers to
Rik van Grol
van Hogendorpstraat 75
2515 NT Den Haag
The Netherlands
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Intermediate Results can be found in CFF 40.
Torsten Sillke,
Crossless L-Tromino Rectangles -- Contest 28 Result
C(ubism)F(or)F(un) 40 (June 1996) 26-27