Model response

Step $1$

Let's analyze the game. We have a row of $117$ squares. On each turn, a player can

delete either one or two consecutive squares. The game ends when there are no

more squares left. The player who makes the last move wins.

Let's consider smaller cases to see if we can find a pattern.

Step $2$

Step $3$

Case n$=1$ : Player $1$ deletes the single square and wins.

Case n$=2$ : Player $1$ deletes both squares and wins.

Case n$=3$ : Player $1$ deletes one square, leaving two. Player $2$ deletes both and wins. If

Player $1$ deletes two squares, Player $2$ deletes the remaining one and wins. So Player

$2$ wins.

Case n$=4$ : Player $1$ deletes one square, leaving three. Player $2$ is in the n$=3$ case, so

Player $1$ wins.

Case n$=5$ : Player $1$ deletes two squares, leaving three. Player $2$ is in the n$=3$ case, so

Player $1$ wins.

Let's summarize our findings:

n$=1$ : Player $1$ wins

Step $4$

n$=2$ : Player $1$ wins

n$=3$ : Player $2$ wins

n$=4$: Player $1$ wins

n$=5$ : Player $1$ wins

which step is incorrect?