A353103 Solution to Forest of Numbers (Bosque de Números) puzzle for Opaque Rooks starting with numbers 1 and 2 for an n X n square grid (see Comments).

3, 7, 9, 12, 16, 21, 25, 32, 37

Offset: 2

Author

Rodolfo Kurchan, Apr 23 2022

Keywords

• nonn
• more

Comments

Start with an n X n square grid. Each cell has neighbors horizontally and vertically. 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 Rook attack in the same row and column must equal k. Then a(n) is the maximum m that can be achieved.

Examples

			Solution for a(5) = 12 from Rodolfo Kurchan:
  +---+---+---+---+---+
  | 1 |   |   | 4 | 3 |
  +---+---+---+---+---+
  | 6 |   |   |   | 5 |
  +---+---+---+---+---+
  |   |   |   | 11| 7 |
  +---+---+---+---+---+
  |   |   |   |   | 9 |
  +---+---+---+---+---+
  | 8 | 10| 12|   | 2 |
  +---+---+---+---+---+
Solutions for a(2) to a(6) from Rodolfo Kurchan.
Solutions for a(7) to a(10) from Giorgio Vecchi.
		

Links

• Rodolfo Kurchan, Puzzle Fun, Problems, Forest of Numbers

Crossrefs

Cf. A350627, A352814, A353070, A353093.