90 lines
5.7 KiB
HTML
90 lines
5.7 KiB
HTML
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<h2>Amazing Mazes!</h2><div class="info" style="cursor:help;width:200px;margin-bottom:10px;"><h3>Problem 380</h3><span style="width:300px;color:#666;">Published on Saturday, 14th April 2012, 02:00 pm; Solved by 318</span></div>
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An m<img src='images/symbol_times.gif' width='9' height='9' alt='×' border='0' style='vertical-align:middle;' />n maze is an m<img src='images/symbol_times.gif' width='9' height='9' alt='×' border='0' style='vertical-align:middle;' />n rectangular grid with walls placed between grid cells such that there is exactly one path from the top-left square to any other square. <BR />The following are examples of a 9<img src='images/symbol_times.gif' width='9' height='9' alt='×' border='0' style='vertical-align:middle;' />12 maze and a 15<img src='images/symbol_times.gif' width='9' height='9' alt='×' border='0' style='vertical-align:middle;' />20 maze:
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Let C(m,n) be the number of distinct m<img src='images/symbol_times.gif' width='9' height='9' alt='×' border='0' style='vertical-align:middle;' />n mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.
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It can be verified that C(1,1) = 1, C(2,2) = 4, C(3,4) = 2415, and C(9,12) = 2.5720e46 (in scientific notation rounded to 5 significant digits).<BR />
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Find C(100,500) and write your answer in scientific notation rounded to 5 significant digits.
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When giving your answer, use a lowercase e to separate mantissa and exponent.
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E.g. if the answer is 1234567891011 then the answer format would be 1.2346e12.
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