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BEBRAS 2025 Grade 9-10 Round 2 Ext Question 5

BEBRAS · BEBRAS 2025 Grade 9-10 Round 2 Ext

Question 5

A Berukone board is a square grid of circles, some numbered. Join equal numbers by paths along grid links through unnumbered circles. Each numbered circle must have exactly one selected incident link, and each unnumbered circle at most two. The source gives one solvable and one impossible 3 × 3 example.

Question illustration

How many of the following four boards, numbered 1–4 from left to right, are impossible?

Question illustration
  1. 0
  2. 1
  3. 2
  4. 3