yaworsw/euler-manager

---
:id: 313
:name: Sliding game
:url: https://projecteuler.net/problem=313
:content: |+
  In a sliding game a counter may slide horizontally or vertically into an empty space. The objective of the game is to move the red counter from the top left corner of a grid to the bottom right corner; the space always starts in the bottom right corner. For example, the following sequence of pictures show how the game can be completed in five moves on a 2 by 2 grid.

   ![p313_sliding_game_1.gif]({{ images_dir }}/p313_sliding_game_1.gif)

  Let S(m,n) represent the minimum number of moves to complete the game on an m by n grid. For example, it can be verified that S(5,4) = 25.

   ![p313_sliding_game_2.gif]({{ images_dir }}/p313_sliding_game_2.gif)

  There are exactly 5482 grids for which S(m,n) = p<sup>2</sup>, where p \< 100 is prime.

  How many grids does S(m,n) = p<sup>2</sup>, where p \< 10<sup>6</sup> is prime?