8 XXX : keyholdercaptions

as far as i can tell, 19 is the worst possible answer. as the first case would grant you n orgasms, the function of orgasms is o1(n) = n. in the second case, you are granted 365 / n orgasms, so o2(n) = 365 * 1 / n, or o2(n) = 365 * n ^ -1. adding both of them together and averaging them (as this is stochastics) yields o(n) = 0.5n 0.5 * 365 * n ^ -1 where n is your answer and o(n) the count of orgasms this year. doing some analysis shows that there is a mininum at ca. 19.1 o'(n) = 0.5 -0.5 * 365 * n ^ -2 o''(n) = 365 * n ^ -3 o'(n) = 0 <=> 0.5 - 0.5 * 365 * n ^ - 2 = 0 0.5 * 365 * n ^ -2 = 0.5 n ^ -2 = 0.0027398 n = 19.1049733 o''(19.1049733) = 0.05321475 as n approaches 0 or positive infinity, o(n) also approaches infinity. meaning you should either go with the smallest or the highest possible number. edit: reddit mobile messed with the formatting. oh well