A353093 Solution to Forest of Numbers (Bosque de Números) puzzle for Opaque Queens starting with numbers 1 and 2 for an n X n square grid (see Comments).

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

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 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.

Links

Table of n, a(n) for n=2..8.

Rodolfo Kurchan, Puzzle Fun, Problems, Forest of Numbers

Example

Solution for a(5) = 13 from Daniel Valdano:
  +---+---+---+---+---+
  | 12| 4 | 8 |   |   |
  +---+---+---+---+---+
  | 7 | 1 | 3 |   | 10|
  +---+---+---+---+---+
  |   |   | 6 |   |   |
  +---+---+---+---+---+
  |   | 9 | 2 | 13| 5 |
  +---+---+---+---+---+
  |   | 11|   |   |   |
  +---+---+---+---+---+
Solution for a(6) = 16 from Daniel Valdano.
Solution for a(7) = 20 from Giorgio Vecchi.
Solution for a(8) = 23 from Giorgio Vecchi.

Crossrefs

Cf. A352814, A350627, A353070.

Sequence in context: A356469 A028433 A310051 * A080667 A277722 A190007

Adjacent sequences: A353090 A353091 A353092 * A353094 A353095 A353096

Keyword

nonn,more

Author

Rodolfo Kurchan, Apr 22 2022

Status

approved