A379589 Maximum number of connections for a 4 X n rectangle.
1, 31, 800, 6466, 60778, 441492, 3216584, 18693320
Offset: 2
Examples
For n = 2 with the board +---+---+ | 1 | 1 | +---+---+ | 2 | 2 | +---+---+ | 3 | 3 | +---+---+ | 4 | 4 | +---+---+ There is only 1 solution being the squares with these letters: +---+---+ | A | B | +---+---+ | C | D | +---+---+ | E | F | +---+---+ | G | H | +---+---+ Solution: 1) AB - CD - EF - GH There is one solution so a(2) = 1. . For n = 3 with the board +---+---+---+ | 1 | 2 | 2 | +---+---+---+ | 1 | 2 | 2 | +---+---+---+ | 3 | 4 | 4 | +---+---+---+ | 3 | 4 | 4 | +---+---+---+ the maximum number of solutions is 31 being the squares with these letters: +---+---+---+ | A | B | C | +---+---+---+ | D | E | F | +---+---+---+ | G | H | I | +---+---+---+ | J | K | L | +---+---+---+ Solutions: 1) AD - GJ - BC - HEFILK 2) AD - GJ - BC - IFEHKL 3) AD - GJ - BC - KHEFIL 4) AD - GJ - KL - EHIFCB 5) AD - GJ - KL - FIHEBC 6) AD - GJ - KL - BEHIFC 7) AD - GJ - BCFE - HILK 8) AD - GJ - BCFE - ILKH 9) AD - GJ - BCFE - LKHI 10) AD - GJ - BCFE - KHIL 11) AD - GJ - CFEB - HILK 12) AD - GJ - CFEB - ILKH 13) AD - GJ - CFEB - LKHI 14) AD - GJ - CFEB - KHIL 15) AD - GJ - FEBC - HILK 16) AD - GJ - FEBC - ILKH 17) AD - GJ - FEBC - LKHI 18) AD - GJ - FEBC - KHIL 19) AD - GJ - EBCF - HILK 20) AD - GJ - EBCF - ILKH 21) AD - GJ - EBCF - LKHI 22) AD - GJ - EBCF - KHIL 23) ABED - GJ - CF - HILK 24) ABED - GJ - CF - ILKH 25) ABED - GJ - CF - LKHI 26) ABED - GJ - CF - KHIL 27) GHKJ - AD - IL - BCFE 28) GHKJ - AD - IL - CFEB 29) GHKJ - AD - IL - FEBC 30) GHKJ - AD - IL - EBCF 31) ABED - GHKJ - CF - IL There are 31 solutions so a(3) = 31.
Links
- Rodolfo Kurchan and Claudio Meller, Number Connections, Puzzle Fun, Problems (2024).
Comments