Problem 1319. Leap years on other planets

  • Created by Tim

A year is a leap year if it is divisible by 4, but not if it is divisible by 100, unless it is also divisible by 400. This means the average length of a calendar year is

    365 + 1/4 - 1/100 + 1/400 = 365.2425 days

which approximately matches the length of an actual year (the number of days it takes the earth to go around the sun once).

Given p, the length of a year on another planet in units of days on that planet, and given that normal years have N days and leap years have N+1 days, where N=floor(p), find integer vector m>0 defining leap years [years divisible by m(1) are leap years, but years divisible by m(2) are not, unless they are divisible by m(3), but then not if they are divisible by m(4), etc.] so that

   p = N + 1/m(1) - 1/m(2) + 1/m(3) - 1/m(4) + ...

Include enough terms so that this is correct to four decimal places. Note that m(i+1) should be an integer multiple of m(i). Results are not necessarily unique. For example, if p=365.2425 then m=[4 100 400] is an exact answer, but m=[4 132 13068] also could be used (and [4 132] gives 365.2424, a better approximation than [4 100], which gives 365.2400).

Solution Stats

60.67% Correct | 39.33% Incorrect
Last Solution submitted on Oct 03, 2023

Problem Comments

Solution Comments

Show comments

Problem Recent Solvers40

Suggested Problems

More from this Author11

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!