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fix(curriculum): clean-up Project Euler 281-300 (#42922)

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* fix: clean-up Project Euler 281-300

* fix: missing image extension

* fix: missing power

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

* fix: missing subscript

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>

Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
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gikf
2021-07-22 05:38:46 +02:00
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commit 47fc3c6761
20 changed files with 238 additions and 169 deletions
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22
curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-289-eulerian-cycles.md
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@ -8,24 +8,26 @@ dashedName: problem-289-eulerian-cycles
# --description--
Let C(x,y) be a circle passing through the points (x, y), (x, y+1), (x+1, y) and (x+1, y+1).
Let $C(x,y)$ be a circle passing through the points ($x$, $y$), ($x$, $y + 1$), ($x + 1$, $y$) and ($x + 1$, $y + 1$).
For positive integers m and n, let E(m,n) be a configuration which consists of the m·n circles: { C(x,y): 0 ≤ x &lt; m, 0 ≤ y &lt; n, x and y are integers }
For positive integers $m$ and $n$, let $E(m,n)$ be a configuration which consists of the $m·n$ circles: { $C(x,y)$: $0 ≤ x &lt; m$, $0 ≤ y &lt; n$, $x$ and $y$ are integers }
An Eulerian cycle on E(m,n) is a closed path that passes through each arc exactly once. Many such paths are possible on E(m,n), but we are only interested in those which are not self-crossing: A non-crossing path just touches itself at lattice points, but it never crosses itself.
An Eulerian cycle on $E(m,n)$ is a closed path that passes through each arc exactly once. Many such paths are possible on $E(m,n)$, but we are only interested in those which are not self-crossing: A non-crossing path just touches itself at lattice points, but it never crosses itself.
The image below shows E(3,3) and an example of an Eulerian non-crossing path.
The image below shows $E(3,3)$ and an example of an Eulerian non-crossing path.
Let L(m,n) be the number of Eulerian non-crossing paths on E(m,n). For example, L(1,2) = 2, L(2,2) = 37 and L(3,3) = 104290.
<img class="img-responsive center-block" alt="Eulerian cycle E(3, 3) and Eulerian non-crossing path" src="https://cdn.freecodecamp.org/curriculum/project-euler/eulerian-cycles.gif" style="background-color: white; padding: 10px;">
Find L(6,10) mod 1010.
Let $L(m,n)$ be the number of Eulerian non-crossing paths on $E(m,n)$. For example, $L(1,2) = 2$, $L(2,2) = 37$ and $L(3,3) = 104290$.
Find $L(6,10)\bmod {10}^{10}$.
# --hints--
`euler289()` should return 6567944538.
`eulerianCycles()` should return `6567944538`.
```js
assert.strictEqual(euler289(), 6567944538);
assert.strictEqual(eulerianCycles(), 6567944538);
```
# --seed--
@ -33,12 +35,12 @@ assert.strictEqual(euler289(), 6567944538);
## --seed-contents--
```js
function euler289() {
function eulerianCycles() {
return true;
}
euler289();
eulerianCycles();
```
# --solutions--