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id	challengeType	title	forumTopicId
5900f4fa1000cf542c51000d	5	Problem 398: Cutting rope	302063

Description

Inside a rope of length n, n-1 points are placed with distance 1 from each other and from the endpoints. Among these points, we choose m-1 points at random and cut the rope at these points to create m segments.

Let E(n, m) be the expected length of the second-shortest segment. For example, E(3, 2) = 2 and E(8, 3) = 16/7. Note that if multiple segments have the same shortest length the length of the second-shortest segment is defined as the same as the shortest length.

Find E(107, 100). Give your answer rounded to 5 decimal places behind the decimal point.

Instructions

Tests

tests:
  - text: <code>euler398()</code> should return 2010.59096.
    testString: assert.strictEqual(euler398(), 2010.59096);

Challenge Seed

function euler398() {
  // Good luck!
  return true;
}

euler398();

Solution

// solution required

1.2 KiB Raw Blame History