2019 OIM Problems/Problem 5

Revision as of 13:12, 14 December 2023 by Tomasdiaz (talk | contribs) (Created page with "== Problem == Don Miguel places a game piece on one of the <math>(n + 1)^2</math> vertices defined by a <math>n \times n</math> board. A ''move'' consists of moving the piece...")
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Problem

Don Miguel places a game piece on one of the $(n + 1)^2$ vertices defined by a $n \times n$ board. A move consists of moving the piece from the vertex where it is located at an adjacent vertex in one of the eight possible directions: $\uparrow, \downarrow, \to, \gets, \nearrow, \searrow, \nwarrow, \swarrow,$ as long as it does not go off the board. A tour is a sequence of moves such that the game pieces has been at each of the $(n + 1)^2$ vertices exactly only once. What is the greatest number of diagonal moves ($\nearrow, \searrow, \nwarrow, \swarrow,$) that you can have in a tour?

~translated into English by Tomas Diaz. ~orders@tomasdiaz.com

Solution

This problem needs a solution. If you have a solution for it, please help us out by adding it.

See also

OIM Problems and Solutions