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A353070 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
3, 5, 8, 10, 13, 15, 17, 19 (list; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=2..9.

Rodolfo Kurchan, Puzzle Fun, Problems, Forest of Numbers

EXAMPLE

Solutions for 5 <= n <= 8 from Pontus von Brömssen:

  +---+---+---+---+---+

  | 1 |   | 2 | 8 |   |

  +---+---+---+---+---+

  | 9 | 3 | 5 |   |   |

  +---+---+---+---+---+

  |   |   |   |   | 6 |

  +---+---+---+---+---+

  |   |10 |   |   |   |

  +---+---+---+---+---+

  |   | 7 |   |   | 4 |

  +---+---+---+---+---+

.

  +---+---+---+---+---+---+

  | 1 | 9 |   | 8 |   |   |

  +---+---+---+---+---+---+

  |   |   |   | 7 |   |12 |

  +---+---+---+---+---+---+

  |10 |   |   |   |   |   |

  +---+---+---+---+---+---+

  |   |   | 6 |   |   | 2 |

  +---+---+---+---+---+---+

  | 5 |   |   |   |11 |   |

  +---+---+---+---+---+---+

  | 4 |   |13 |   |   | 3 |

  +---+---+---+---+---+---+

.

  +---+---+---+---+---+---+---+

  |   | 8 |   | 6 |   |   |   |

  +---+---+---+---+---+---+---+

  |   |11 | 2 |   |   |   |   |

  +---+---+---+---+---+---+---+

  |   |   |   |   | 5 |   |15 |

  +---+---+---+---+---+---+---+

  | 3 |   |   | 1 |   |   |10 |

  +---+---+---+---+---+---+---+

  |14 |   |   |   |   |   |   |

  +---+---+---+---+---+---+---+

  | 7 |   |12 |   |   |   |   |

  +---+---+---+---+---+---+---+

  | 4 |   |   |   | 9 |13 |   |

  +---+---+---+---+---+---+---+

.

  +---+---+---+---+---+---+---+---+

  | 1 | 3 |   |12 | 6 |   | 2 |   |

  +---+---+---+---+---+---+---+---+

  | 4 |   |   |   |   |   |11 |   |

  +---+---+---+---+---+---+---+---+

  |   |   | 7 |   |15 |   |   |   |

  +---+---+---+---+---+---+---+---+

  |   |   |   |   |   |   |   |14 |

  +---+---+---+---+---+---+---+---+

  |   |13 |   |   |   |   |   |   |

  +---+---+---+---+---+---+---+---+

  |10 |   |   |   |   |   | 5 |   |

  +---+---+---+---+---+---+---+---+

  |   |   |16 |   |   | 9 |   |   |

  +---+---+---+---+---+---+---+---+

  |   |   |   |   |   |17 |   | 8 |

  +---+---+---+---+---+---+---+---+

Solution for a(9) = 19 from Giorgio Vecchi

CROSSREFS

Cf. A352814, A350627.

Sequence in context: A033033 A211704 A275813 * A080754 A198083 A195168

Adjacent sequences:  A353067 A353068 A353069 * A353071 A353072 A353073

KEYWORD

nonn,more

AUTHOR

Rodolfo Kurchan, Apr 21 2022

STATUS

approved

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Last modified August 13 08:18 EDT 2022. Contains 356079 sequences. (Running on oeis4.)