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* 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>
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id, title, challengeType, forumTopicId, dashedName
| id | title | challengeType | forumTopicId | dashedName |
|---|---|---|---|---|
| 5900f4331000cf542c50ff45 | Problem 198: Ambiguous Numbers | 5 | 301836 | problem-198-ambiguous-numbers |
--description--
A best approximation to a real number x for the denominator bound d is a rational number \frac{r}{s} (in reduced form) with s ≤ d, so that any rational number \frac{p}{q} which is closer to x than \frac{r}{s} has q > d.
Usually the best approximation to a real number is uniquely determined for all denominator bounds. However, there are some exceptions, e.g. \frac{9}{40} has the two best approximations \frac{1}{4} and \frac{1}{5} for the denominator bound 6. We shall call a real number x ambiguous, if there is at least one denominator bound for which x possesses two best approximations. Clearly, an ambiguous number is necessarily rational.
How many ambiguous numbers x = \frac{p}{q}, 0 < x < \frac{1}{100}, are there whose denominator q does not exceed {10}^8?
--hints--
ambiguousNumbers() should return 52374425.
assert.strictEqual(ambiguousNumbers(), 52374425);
--seed--
--seed-contents--
function ambiguousNumbers() {
return true;
}
ambiguousNumbers();
--solutions--
// solution required