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Frosted Board

Puzzle #35: Dots and Boxes

  • DifficultyHard
  • To moveDark
  • TaskTake 15 of 25
  • Main line30 half-moves

Dark to move on the 5 × 5 board. 30 of 60 lines are drawn, Dark has 0 boxes and Light 0.

25 boxes are still unclaimed. With best play you can take 15 of them, 5 more than the opponent gets, and exactly one line achieves that.

What the position is about

  • double-dealing — The key line declines the last boxes of a chain so that the opponent has to open the next one.
  • keep control — With best play you stay in control and collect more than half of what is left.

Finding the way in

On 5×5 the chains are long and the loops expensive. Work out the value of opening each component, and open the cheapest one for the opponent to take.

Take your time. There is no clock on the result, and a wrong move is simply taken back so you can look again.

Show the first move

Start with a6-b6. Played out against the stiffest resistance, the whole line goes: a6-b6 a5-b5 a1-b1 a2-b2 a3-a4 a3-b3 d1-e1 d2-e2 f2-f3 e2-e3 e1-f1 f1-f2 e5-e6 d6-e6 e6-f6 b3-c3 b4-c4 b5-c5 c5-c6 c5-d5 c4-d4 d3-d4 d4-e4 e4-e5 f3-f4 e4-f4 b2-c2 c1-c2 c2-d2 c2-c3.

Solve it and the next puzzle of the same game is one tap away. Your solved puzzles are ticked in the list, in this browser only.