43 lines
1.1 KiB
Markdown
43 lines
1.1 KiB
Markdown
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---
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id: 5900f4331000cf542c50ff45
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title: 'Problem 198: Ambiguous Numbers'
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challengeType: 5
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forumTopicId: 301836
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dashedName: problem-198-ambiguous-numbers
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---
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# --description--
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A best approximation to a real number x for the denominator bound d is a rational number r/s (in reduced form) with s ≤ d, so that any rational number p/q which is closer to x than r/s has q > d.
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Usually the best approximation to a real number is uniquely determined for all denominator bounds. However, there are some exceptions, e.g. 9/40 has the two best approximations 1/4 and 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.
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How many ambiguous numbers x = p/q, 0 < x < 1/100, are there whose denominator q does not exceed 108?
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# --hints--
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`euler198()` should return 52374425.
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```js
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assert.strictEqual(euler198(), 52374425);
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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 euler198() {
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return true;
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}
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euler198();
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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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