freeCodeCamp/curriculum/challenges/english/08-coding-interview-prep/project-euler/problem-198-ambiguous-numbers.english.md

id	challengeType	title
5900f4331000cf542c50ff45	5	Problem 198: Ambiguous Numbers

Description

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.

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.

How many ambiguous numbers x = p/q, 0 < x < 1/100, are there whose denominator q does not exceed 108?

Instructions

Tests

tests:
  - text: <code>euler198()</code> should return 52374425.
    testString: assert.strictEqual(euler198(), 52374425);

Challenge Seed

function euler198() {
  // Good luck!
  return true;
}

euler198();

Solution

// solution required