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

%I #16 Apr 29 2022 15:53:26

%S 3,6,10,13,16,20,23

%N Solution to Forest of Numbers (Bosque de NĂºmeros) puzzle for Opaque 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 that a Chess Queen attack 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 Solution for a(5) = 13 from Daniel Valdano:

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

%e | 12| 4 | 8 | | |

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

%e | 7 | 1 | 3 | | 10|

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

%e | | | 6 | | |

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

%e | | 9 | 2 | 13| 5 |

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

%e | | 11| | | |

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

%e Solution for a(6) = 16 from Daniel Valdano.

%e Solution for a(7) = 20 from Giorgio Vecchi.

%e Solution for a(8) = 23 from Giorgio Vecchi.

%Y Cf. A352814, A350627, A353070.

%K nonn,more

%O 2,1

%A _Rodolfo Kurchan_, Apr 22 2022