The OEIS is supported by the many generous donors to the OEIS Foundation. Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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

%I

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

%N 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).

%C 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.

%H Rudolfo Kurchan, <a href="http://www.puzzlefun.online">Puzzle Fun</a>

%e 4 X 4 solution with m = a(4) = 12 from Hector San Segundo:

%e +---+---+---+---+

%e | | 10| 3 | 8 |

%e +---+---+---+---+

%e | | 6| 1| 4|

%e +---+---+---+---+

%e | | 2| | 5|

%e +---+---+---+---+

%e | 11| 9| 7| 12|

%e +---+---+---+---+

%e 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.

%e 5 X 5 solution with m = a(5) = 19 from _Pontus von Brömssen_:

%e +---+---+---+---+---+

%e | 5| 6| 7| 8| 18|

%e +---+---+---+---+---+

%e | 11| | 1| | 10|

%e +---+---+---+---+---+

%e | 14| | 19| 2| 16|

%e +---+---+---+---+---+

%e | | 3| 9| 4| |

%e +---+---+---+---+---+

%e | 15| 12| | 13| 17|

%e +---+---+---+---+---+

%e .

%e One of 10 6 X 6 solutions (up to rotations and reflections) with m = a(6) = 25 from _Pontus von Brömssen_, Apr 15 2022:

%e +---+---+---+---+---+---+

%e | 22| 1| 15| 19| | 20|

%e +---+---+---+---+---+---+

%e | 7| 14| | | 4| 16|

%e +---+---+---+---+---+---+

%e | | 6| | 21| | 12|

%e +---+---+---+---+---+---+

%e | 17| | 9| | 8| 25|

%e +---+---+---+---+---+---+

%e | | 11| | 3| 5| |

%e +---+---+---+---+---+---+

%e | 24| 13| 2| 10| 18| 23|

%e +---+---+---+---+---+---+

%e .

%e a(7) = 34 from Giorgio Vecchi.

%Y Cf. A350627.

%K nonn,more

%O 1,2

%A _Rodolfo Kurchan_, Apr 04 2022

%E a(6) corrected by _Pontus von Brömssen_, Apr 15 2022

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 15 00:08 EDT 2022. Contains 356122 sequences. (Running on oeis4.)