Xi'an's Og

A riddle from the Riddler with a variation on the theme of breaking sticks: Given a stick of length L, what is the optimal manner to break said stick to achieve a maximal product of the individual lengths? While the pen & paper resolution is a one-line back-of-the-envelope calculation, with an impact of the length L, obviously,  a quick R code leads to an approximate solution:

mw=function(k=2,l=10,T=1e6){
  a=matrix(runif(T*k),k)
  for(i in 1:T)F=max(F,prod(l*a[,i]/sum(a[,i])))
  return(F)}

with increasing inaccuracy when L grows, obviously.

This entry was posted on July 6, 2021 at 12:21 am and is filed under Kids, pictures, R with tags Dirichlet processes, mathematical puzzle, R, stick breaking process, The Riddler. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.