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id	title	challengeType	forumTopicId	dashedName
5900f4e81000cf542c50fffb	Problem 380: Amazing Mazes!	5	302044	problem-380-amazing-mazes

--description--

An m×n maze is an m×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. The following are examples of a 9×12 maze and a 15×20 maze:

Let C(m, n) be the number of distinct m×n mazes. Mazes which can be formed by rotation and reflection from another maze are considered distinct.

It can be verified that C(1, 1) = 1, C(2, 2) = 4, C(3, 4) = 2415, and C(9, 12) = 2.5720\mathrm{e}\\,46 (in scientific notation rounded to 5 significant digits).

Find C(100, 500) and write your answer as a string in scientific notation rounded to 5 significant digits.

When giving your answer, use a lowercase e to separate mantissa and exponent. E.g. if the answer is 1234567891011 then the answer format would be the string 1.2346e12.

--hints--

amazingMazes() should return a string.

assert(typeof amazingMazes() === 'string');

amazingMazes() should return the string 6.3202e25093.

assert.strictEqual(amazingMazes(), '6.3202e25093');

--seed--

--seed-contents--

function amazingMazes() {

  return true;
}

amazingMazes();

--solutions--

// solution required

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