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

2,1

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.

Links

Table of n, a(n) for n=2..10.

Rodolfo Kurchan, Puzzle Fun, Problems, Forest of Numbers

Example

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.

Crossrefs

Cf. A350627, A352814, A353070, A353093.

Sequence in context: A190742 A289906 A190752 * A087064 A189561 A087550

Adjacent sequences: A353100 A353101 A353102 * A353104 A353105 A353106

Keyword

nonn,more

Author

Rodolfo Kurchan, Apr 23 2022

Status

approved