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Moving South and East



The southeast puzzle is played on a semi-infinite chessboard, starting at its northwest (top left) corner. There are three rules:

  1. In the starting position, one piece is placed in the northwest-most square, as shown in (a).
  2. It is not permitted for more than one piece to be on any given square.
  3. At each step, you remove one piece from the board, and replace it with two pieces, one in the square immediately to the East, and one in the the square immediately to the South, as illustrated in (b). Every such step increases the number of pieces on the board by one.

After move (b) has been made, either piece may be selected for the next move. © shows the outcome of moving the lower piece. At the next move, either the lowest piece or the middle piece of the three may be selected; the uppermost piece may not be selected, since that would violate rule 2. At move (d) we have selected the middle piece. Now any of the pieces may be moved, except for the leftmost piece.


Puzzle: Is it possible to obtain a position in which all of the ten squares closest to the northwest corner, marked in the rightmost figure (z), are empty?

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