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CEMC Gauss (Grade 8), 1999

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

A game is played on the board shown. In this game, a player can move three places in any direction (up, down, right or left) and then can move two places in a direction perpendicular to the first move. If a player starts at $S$ , which position on the board ( $P$ , $Q$ , $R$ , $T$ , or $W$ ) cannot be reached through any sequence of moves?

(A) $P$ (B) $Q$ (C) $R$ (D) $T$ (E) $W$

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