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BEBRAS 2025 Grade 11-12 Round 2 Ext Question 2

BEBRAS · BEBRAS 2025 Grade 11-12 Round 2 Ext

Question 2

A Berukone board is a square grid of circles, some containing numbers. Connect equal-numbered circles by paths through unnumbered circles, following the grid links. Each numbered circle must have exactly one selected incident link and each unnumbered circle at most two. Here are a solvable board and an impossible board.

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How many of the following four boards cannot be solved?
Board 1:

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Board 2:

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Board 3:

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Board 4:

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  1. 0
  2. 1
  3. 2
  4. 3