MathDB

Shikaku and his son Shikamaru must climb a staircase that has

2022

steps; the steps are listed

1

2

...

2022

and the floor is considered step

0

. This bores them both a lot, so so they decide to organize a game. They begin by tying a rope between them, so that At most they can be separated from each other by a distance of

7

steps, that is, if they are in the steps

m

and

n

, then it must always be true that

|m-n| \le 7

. For the game they establish the following rules: a) They move alternately in turns. b) In his corresponding turn, the player must move to a higher step than in the one that (the same) was previously. c) If a player has just moved to the

n

-th step, then on the next turn the other player cannot be moved to any of the steps

n-1

n

n + 1

, except when it is for reach the last step. d) Whoever reaches the last step (listed with

2022

) wins. Shikamaru is bored to start, so his father starts. Determine which of the two players has a winning strategy and describe it.

Problem Statement