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).

3, 5, 8, 10, 13, 15, 17, 19

Offset: 2

Author

Rodolfo Kurchan, Apr 21 2022

Keywords

• nonn
• more

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.

Examples

			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
		

Links

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

Crossrefs

Cf. A352814, A350627.