yaworsw/euler-manager

---
:id: 331
:name: Cross flips
:url: https://projecteuler.net/problem=331
:content: "<var>N</var>×<var>N</var> disks are placed on a square game board. Each
  disk has a black side and white side.\n\nAt each turn, you may choose a disk and
  flip all the disks in the same row and the same column as this disk: thus 2×<var>N</var>-1
  disks are flipped. The game ends when all disks show their white side. The following
  example shows a game on a 5×5 board.\n\n ![p331_crossflips3.gif]({{ images_dir }}/p331_crossflips3.gif)\n\nIt
  can be proven that 3 is the minimal number of turns to finish this game.\n\nThe
  bottom left disk on the <var>N</var>×<var>N</var> board has coordinates (0,0);  \nthe
  bottom right disk has coordinates (<var>N</var>-1,0) and the top left disk has coordinates
  (0,<var>N</var>-1).\n\nLet C<sub><var>N</var></sub> be the following configuration
  of a board with <var>N</var>×<var>N</var> disks:  \nA disk at (<var>x</var>,<var>y</var>)
  satisfying ![p331_crossflips1.gif]({{ images_dir }}/p331_crossflips1.gif), shows
  its black side; otherwise, it shows its white side. C<sub>5</sub> is shown above.\n\nLet
  T(<var>N</var>) be the minimal number of turns to finish a game starting from configuration
  C<sub><var>N</var></sub> or 0 if configuration C<sub><var>N</var></sub> is unsolvable.
  \ \nWe have shown that T(5)=3. You are also given that T(10)=29 and T(1 000)=395253.\n\nFind
  ![p331_crossflips2.gif]({{ images_dir }}/p331_crossflips2.gif).\n\n"