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id	challengeType	title	forumTopicId
5900f3861000cf542c50fe99	5	Problem 26: Reciprocal cycles	301908

Description

A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:

¹/₂ = 0.5

¹/₃ = 0.(3)

¹/₄ = 0.25

¹/₅ = 0.2

¹/₆ = 0.1(6)

¹/₇ = 0.(142857)

¹/₈ = 0.125

¹/₉ = 0.(1)

¹/₁₀ = 0.1

Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that ¹/₇ has a 6-digit recurring cycle. Find the value of d < n for which ¹/_d contains the longest recurring cycle in its decimal fraction part.

Instructions

Tests

tests:
  - text: <code>reciprocalCycles(700)</code> should return 659.
    testString: assert(reciprocalCycles(700) == 659);
  - text: <code>reciprocalCycles(800)</code> should return 743.
    testString: assert(reciprocalCycles(800) == 743);
  - text: <code>reciprocalCycles(900)</code> should return 887.
    testString: assert(reciprocalCycles(900) == 887);
  - text: <code>reciprocalCycles(1000)</code> should return 983.
    testString: assert(reciprocalCycles(1000) == 983);

Challenge Seed

function reciprocalCycles(n) {
  // Good luck!
  return n;
}

reciprocalCycles(1000);

Solution

// solution required

1.9 KiB Raw Blame History