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Solution to Forest of Numbers (Bosque de Números) puzzle for Transparent Queens starting with numbers 1 and 2 for an n X n square grid (see Comments).
2

%I #21 Apr 29 2022 15:53:33

%S 3,5,8,10,13,15,17,19

%N Solution to Forest of Numbers (Bosque de Números) puzzle for Transparent Queens starting with numbers 1 and 2 for an n X n square grid (see Comments).

%C Start with an n X n square grid. Each cell has neighbors horizontally, vertically and diagonally. Place the numbers 1 and 2 anywhere. Now place the numbers 3, 4, ..., m in order, subject to the rule that when you place k, the sum of the numbers in the same row, column and diagonal must equal k. Then a(n) is the maximum m that can be achieved.

%H Rodolfo Kurchan, <a href="https://www.puzzlefun.online/problems">Puzzle Fun, Problems, Forest of Numbers</a>

%e Solutions for 5 <= n <= 8 from _Pontus von Brömssen_:

%e +---+---+---+---+---+

%e | 1 | | 2 | 8 | |

%e +---+---+---+---+---+

%e | 9 | 3 | 5 | | |

%e +---+---+---+---+---+

%e | | | | | 6 |

%e +---+---+---+---+---+

%e | |10 | | | |

%e +---+---+---+---+---+

%e | | 7 | | | 4 |

%e +---+---+---+---+---+

%e .

%e +---+---+---+---+---+---+

%e | 1 | 9 | | 8 | | |

%e +---+---+---+---+---+---+

%e | | | | 7 | |12 |

%e +---+---+---+---+---+---+

%e |10 | | | | | |

%e +---+---+---+---+---+---+

%e | | | 6 | | | 2 |

%e +---+---+---+---+---+---+

%e | 5 | | | |11 | |

%e +---+---+---+---+---+---+

%e | 4 | |13 | | | 3 |

%e +---+---+---+---+---+---+

%e .

%e +---+---+---+---+---+---+---+

%e | | 8 | | 6 | | | |

%e +---+---+---+---+---+---+---+

%e | |11 | 2 | | | | |

%e +---+---+---+---+---+---+---+

%e | | | | | 5 | |15 |

%e +---+---+---+---+---+---+---+

%e | 3 | | | 1 | | |10 |

%e +---+---+---+---+---+---+---+

%e |14 | | | | | | |

%e +---+---+---+---+---+---+---+

%e | 7 | |12 | | | | |

%e +---+---+---+---+---+---+---+

%e | 4 | | | | 9 |13 | |

%e +---+---+---+---+---+---+---+

%e .

%e +---+---+---+---+---+---+---+---+

%e | 1 | 3 | |12 | 6 | | 2 | |

%e +---+---+---+---+---+---+---+---+

%e | 4 | | | | | |11 | |

%e +---+---+---+---+---+---+---+---+

%e | | | 7 | |15 | | | |

%e +---+---+---+---+---+---+---+---+

%e | | | | | | | |14 |

%e +---+---+---+---+---+---+---+---+

%e | |13 | | | | | | |

%e +---+---+---+---+---+---+---+---+

%e |10 | | | | | | 5 | |

%e +---+---+---+---+---+---+---+---+

%e | | |16 | | | 9 | | |

%e +---+---+---+---+---+---+---+---+

%e | | | | | |17 | | 8 |

%e +---+---+---+---+---+---+---+---+

%e Solution for a(9) = 19 from Giorgio Vecchi

%Y Cf. A352814, A350627.

%K nonn,more

%O 2,1

%A _Rodolfo Kurchan_, Apr 21 2022