1.9 KiB
id | challengeType | title | forumTopicId |
---|---|---|---|
5900f4691000cf542c50ff7c | 5 | Problem 253: Tidying up | 301901 |
Description
Every night, the child's father has to pick up the pieces of the caterpillar that have been scattered across the play room. He picks up the pieces at random and places them in the correct order. As the caterpillar is built up in this way, it forms distinct segments that gradually merge together. The number of segments starts at zero (no pieces placed), generally increases up to about eleven or twelve, then tends to drop again before finishing at a single segment (all pieces placed).
For example:
Piece Placed Segments So Far121422936434554354……
Let M be the maximum number of segments encountered during a random tidy-up of the caterpillar. For a caterpillar of ten pieces, the number of possibilities for each M is
M Possibilities1512 2250912 31815264 41418112 5144000
so the most likely value of M is 3 and the average value is 385643⁄113400 = 3.400732, rounded to six decimal places.
The most likely value of M for a forty-piece caterpillar is 11; but what is the average value of M? Give your answer rounded to six decimal places.
Instructions
Tests
tests:
- text: <code>euler253()</code> should return 11.492847.
testString: assert.strictEqual(euler253(), 11.492847);
Challenge Seed
function euler253() {
// Good luck!
return true;
}
euler253();
Solution
// solution required