ABC172F

F - Unfair Nim

• 

• Thoughts.

  • competitive game
  • I’m not sure about the weighting between consideration and implementation, but let’s consider it.
    • When there is only one mountain, you win if you get them all.
    • when two mountains are rising
      • If it’s 1,1, you lose.
      • If x,x, no matter how you take it, it will return to the x,x form, so you lose.
      • If not, then you win in the form of x,x
    • when there are three mountains
      • If a,b,b, you win by taking all a’s.
        • So is a,a,a.
      • When a,b,c
        • If you get some number somewhere for taking it, you lose.
        • Three numbers in a row, you lose.
        • If all but c are contiguous, move c to be contiguous and win.
        • If there is a gap before b, count 2. If the total number of gaps is odd, win?
          • No, we can jump the order and attack to fill in the gaps.

• Official Explanation

  • I’m assuming “if the XOR of each number is 0, the latter wins” is known about Nim.

• unAC

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