A352814 Solution to Forest of Numbers (Bosque de Números) puzzle if we start with the numbers 1 through n for an n X n square grid (see Comments).

1, 3, 8, 12, 19, 25, 34

Offset: 1

Author

Rodolfo Kurchan, Apr 04 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 to n anywhere. Now place the numbers n+1, n+2, ..., m in order, subject to the rule that when you place k, the sum of its neighbors must equal k. Then a(n) is the maximum m that can be achieved.

Examples

			4 X 4 solution with m = a(4) = 12 from Hector San Segundo:
  +---+---+---+---+
  |   | 10| 3 | 8 |
  +---+---+---+---+
  |   |  6|  1|  4|
  +---+---+---+---+
  |   |  2|   |  5|
  +---+---+---+---+
  | 11|  9|  7| 12|
  +---+---+---+---+
4 = 1 + 3, 5 = 1 + 4, 6 = 1 + 2 + 3, 7 = 2 + 5, 8 = 1 + 3 + 4, 9 = 2 + 7, 10 = 1 + 3 + 6, 11 = 2 + 9, 12 = 5 + 7.
5 X 5 solution with m = a(5) = 19 from _Pontus von Brömssen_:
  +---+---+---+---+---+
  |  5|  6|  7|  8| 18|
  +---+---+---+---+---+
  | 11|   |  1|   | 10|
  +---+---+---+---+---+
  | 14|   | 19|  2| 16|
  +---+---+---+---+---+
  |   |  3|  9|  4|   |
  +---+---+---+---+---+
  | 15| 12|   | 13| 17|
  +---+---+---+---+---+
.
One of 10 6 X 6 solutions (up to rotations and reflections) with m = a(6) = 25 from _Pontus von Brömssen_, Apr 15 2022:
  +---+---+---+---+---+---+
  | 22|  1| 15| 19|   | 20|
  +---+---+---+---+---+---+
  |  7| 14|   |   |  4| 16|
  +---+---+---+---+---+---+
  |   |  6|   | 21|   | 12|
  +---+---+---+---+---+---+
  | 17|   |  9|   |  8| 25|
  +---+---+---+---+---+---+
  |   | 11|   |  3|  5|   |
  +---+---+---+---+---+---+
  | 24| 13|  2| 10| 18| 23|
  +---+---+---+---+---+---+
.
a(7) = 34 from Giorgio Vecchi.
		

Links

• Rudolfo Kurchan, Puzzle Fun

Crossrefs

Cf. A350627.

Extensions

a(6) corrected by Pontus von Brömssen, Apr 15 2022