5a52c229f5
* fix: clean-up Project Euler 181-200 * fix: corrections from review Co-authored-by: Tom <20648924+moT01@users.noreply.github.com> * fix: missing delimiter Co-authored-by: Tom <20648924+moT01@users.noreply.github.com>
47 lines
1.2 KiB
Markdown
47 lines
1.2 KiB
Markdown
---
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id: 5900f42c1000cf542c50ff3f
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title: 'Problem 192: Best Approximations'
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challengeType: 5
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forumTopicId: 301830
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dashedName: problem-192-best-approximations
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---
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# --description--
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Let $x$ be a real number.
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A best approximation to $x$ for the denominator bound $d$ is a rational number $\frac{r}{s}$ in reduced form, with $s ≤ d$, such that any rational number which is closer to $x$ than $\frac{r}{s}$ has a denominator larger than $d$:
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$$|\frac{p}{q} - x| < |\frac{r}{s} - x| ⇒ q > d$$
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For example, the best approximation to $\sqrt{13}$ for the denominator bound $20$ is $\frac{18}{5}$ and the best approximation to $\sqrt{13}$ for the denominator bound $30$ is $\frac{101}{28}$.
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Find the sum of all denominators of the best approximations to $\sqrt{n}$ for the denominator bound ${10}^{12}$, where $n$ is not a perfect square and $1 < n ≤ 100000$.
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# --hints--
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`bestApproximations()` should return `57060635927998344`.
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```js
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assert.strictEqual(bestApproximations(), 57060635927998344);
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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 bestApproximations() {
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return true;
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}
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bestApproximations();
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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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