53 lines
1.5 KiB
Markdown
53 lines
1.5 KiB
Markdown
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---
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id: 5900f5081000cf542c51001a
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title: 'Problem 412: Gnomon numbering'
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challengeType: 5
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forumTopicId: 302081
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dashedName: problem-412-gnomon-numbering
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---
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# --description--
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For integers $m$, $n$ ($0 ≤ n < m$), let $L(m, n)$ be an $m×m$ grid with the top-right $n×n$ grid removed.
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For example, $L(5, 3)$ looks like this:
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<img class="img-responsive center-block" alt="5x5 grid, with removed 3x3 grid from the top-right" src="https://cdn.freecodecamp.org/curriculum/project-euler/gnomon-numbering-1.png" style="background-color: white; padding: 10px;" />
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We want to number each cell of $L(m, n)$ with consecutive integers 1, 2, 3, ... such that the number in every cell is smaller than the number below it and to the left of it.
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For example, here are two valid numberings of $L(5, 3)$:
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<img class="img-responsive center-block" alt="two valid numberings of L(5, 3)" src="https://cdn.freecodecamp.org/curriculum/project-euler/gnomon-numbering-2.png" style="background-color: white; padding: 10px;" />
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Let $LC(m, n)$ be the number of valid numberings of $L(m, n)$. It can be verified that $LC(3, 0) = 42$, $LC(5, 3) = 250\\,250$, $LC(6, 3) = 406\\,029\\,023\\,400$ and $LC(10, 5)\bmod 76\\,543\\,217 = 61\\,251\\,715$.
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Find $LC(10\\,000, 5\\,000)\bmod 76\\,543\\,217$.
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# --hints--
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`gnomonNumbering()` should return `38788800`.
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```js
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assert.strictEqual(gnomonNumbering(), 38788800);
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```
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# --seed--
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## --seed-contents--
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```js
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function gnomonNumbering() {
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return true;
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}
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gnomonNumbering();
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```
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# --solutions--
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```js
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// solution required
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```
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