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fix: clean-up Project Euler 421-440 (#43047)

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2021-07-29 20:14:09 +02:00
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curriculum/challenges/english/10-coding-interview-prep/project-euler/problem-430-range-flips.md
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@ -8,24 +8,26 @@ dashedName: problem-430-range-flips
# --description--
N disks are placed in a row, indexed 1 to N from left to right.
$N$ disks are placed in a row, indexed 1 to $N$ from left to right.
Each disk has a black side and white side. Initially all disks show their white side.
At each turn, two, not necessarily distinct, integers A and B between 1 and N (inclusive) are chosen uniformly at random. All disks with an index from A to B (inclusive) are flipped.
At each turn, two, not necessarily distinct, integers $A$ and $B$ between 1 and $N$ (inclusive) are chosen uniformly at random. All disks with an index from $A$ to $B$ (inclusive) are flipped.
The following example shows the case N = 8. At the first turn A = 5 and B = 2, and at the second turn A = 4 and B = 6.
The following example shows the case $N = 8$. At the first turn $A = 5$ and $B = 2$, and at the second turn $A = 4$ and $B = 6$.
Let E(N, M) be the expected number of disks that show their white side after M turns. We can verify that E(3, 1) = 10/9, E(3, 2) = 5/3, E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893.
<img class="img-responsive center-block" alt="example for N = 8, with first turn A = 5 and B = 2, and second turn A = 4 and B = 6" src="https://cdn.freecodecamp.org/curriculum/project-euler/range-flips.gif" style="background-color: white; padding: 10px;">
Find E(1010, 4000). Give your answer rounded to 2 decimal places behind the decimal point.
Let $E(N, M)$ be the expected number of disks that show their white side after $M$ turns. We can verify that $E(3, 1) = \frac{10}{9}$, $E(3, 2) = \frac{5}{3}$, $E(10, 4) ≈ 5.157$ and $E(100, 10) ≈ 51.893$.
Find $E({10}^{10}, 4000)$. Give your answer rounded to 2 decimal places behind the decimal point.
# --hints--
`euler430()` should return 5000624921.38.
`rangeFlips()` should return `5000624921.38`.
```js
assert.strictEqual(euler430(), 5000624921.38);
assert.strictEqual(rangeFlips(), 5000624921.38);
```
# --seed--
@ -33,12 +35,12 @@ assert.strictEqual(euler430(), 5000624921.38);
## --seed-contents--
```js
function euler430() {
function rangeFlips() {
return true;
}
euler430();
rangeFlips();
```
# --solutions--