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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). 3
1, 3, 8, 12, 19, 25, 34 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

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.

LINKS

Table of n, a(n) for n=1..7.

Rudolfo Kurchan, Puzzle Fun

EXAMPLE

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.

CROSSREFS

Cf. A350627.

Sequence in context: A005660 A086813 A287081 * A294482 A103888 A014255

Adjacent sequences:  A352811 A352812 A352813 * A352815 A352816 A352817

KEYWORD

nonn,more

AUTHOR

Rodolfo Kurchan, Apr 04 2022

EXTENSIONS

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

STATUS

approved

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Last modified June 26 01:42 EDT 2022. Contains 354870 sequences. (Running on oeis4.)