A352621 a(n) is the minimum possible value of the largest number placed in a solution to the Forest of Numbers (Bosque de Números) puzzle if we start with the numbers 1 and 2 in an n X n grid (see Comments).

6, 12, 36, 68, 140

Offset: 2

Author

Rodolfo Kurchan, Mar 24 2022

Keywords

• nonn
• more

Comments

Start with an n X n square grid. Each cell has up to eight neighbors. Place the numbers 1 and 2 in any two cells of the grid. Then place a number in each remaining cell, in increasing order (not necessarily using consecutive integers), and with the rule that when you place the number k in a cell, the sum of the numbers in its neighboring cells must equal k. The goal is to fill the grid in such a way as to minimize the largest number placed.

This is similar to the Stepping Stones problem discussed in A337663, but predates it by more than 20 years.

Computer solutions by Dmitry Kamenetsky.

a(7) = 292, a(8) = 502, a(9) = 787 and a(10) 1391 not yet confirmed to be optimal.

Examples

			4 X 4 = 36 solution by _Rodolfo Kurchan_:
  +---+---+---+---+
  | 33| 21|  5| 28|
  +---+---+---+---+
  | 11|  1|  4| 19|
  +---+---+---+---+
  | 24| 10|  3|  7|
  +---+---+---+---+
  | 36|  2| 22| 32|
  +---+---+---+---+
3 is sum of 1+2, 4=1+3, 5=1+4, 7=3+4, 10=1+2+3+4, 11=1+10, 19=3+4+5+7, 21=1+4+5+11, 22=2+3+7+10.
.
5 X 5 = 68 solution by _Dmitry Kamenetsky_:
  +---+---+---+---+---+
  | 32| 18| 63| 30| 56|
  +---+---+---+---+---+
  | 13|  1|  4| 10| 16|
  +---+---+---+---+---+
  |  9|  3| 39|  6| 54|
  +---+---+---+---+---+
  | 36|  5|  2|  8| 14|
  +---+---+---+---+---+
  | 12|  7| 22| 46| 68|
  +---+---+---+---+---+
		

Links

• Rodolfo Kurchan, Puzzle Fun Forest of Numbers

Crossrefs

Cf. A337663, A350627.