Skip to content / Đến nội dung
ThichHocToan.com

BEBRAS 2023 Grade 5-6 Round 2 Ext Question 15

BEBRAS · BEBRAS 2023 Grade 5-6 Round 2 Ext

Question 15

La Pipopipette is a two-player game. Players take turns drawing a horizontal or vertical segment between consecutive dots, aiming to complete as many squares as possible. Whenever a player completes a 1×1 square, they put their own mark in it and immediately draw another segment. The result depends on the number of squares marked by each player. The picture illustrates a draw on a 3×3 dot grid.

Question illustration

“Lượt” means “Turn”; the dark line denotes A’s move and the gray line B’s move. Alice and Bob are now playing on a 2×3 dot grid. The next picture shows Alice’s first move. On each turn, either player may choose a segment randomly.

Question illustration

Which statement about the outcome is true?
  1. Alice certainly cannot lose.
  2. Bob certainly wins.
  3. A draw is certainly impossible.
  4. All outcomes are possible.