79 lines
5.3 KiB
HTML
79 lines
5.3 KiB
HTML
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<h2>Sliding game</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 313</h3><span style="width:300px;color:#666;">Published on Sunday, 5th December 2010, 04:00 am; Solved by 677</span></div>
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<p>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.</p>
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<div align='center'><img src="project/images/p_313_sliding_game_1.gif" /></div>
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<p>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.</p>
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<div align='center'><img src="project/images/p_313_sliding_game_2.gif" /></div>
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<p>There are exactly 5482 grids for which S(m,n) = p<sup>2</sup>, where p <img src='images/symbol_lt.gif' width='10' height='10' alt='<' border='0' style='vertical-align:middle;' /> 100 is prime.</p>
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<p>How many grids does S(m,n) = p<sup>2</sup>, where p <img src='images/symbol_lt.gif' width='10' height='10' alt='<' border='0' style='vertical-align:middle;' /> 10<sup>6</sup> is prime?</p>
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