**T**he little half puzzle proposed a “dumb’ solution in that players play a minimax strategy. There are 34 starting values less than 100 guaranteeing a sure win to dumb players. If instead the players maximise their choice at each step, the R code looks like this:

solveO=function(n){
if (n<3){ solve=(n==2)}else{
solve=(!(solveO(n-1)))||(!solveO(ceiling(n/2)))}
solve}

and there are now 66 (=100-34, indeed!) starting values for which the starting player can win.

**I**ncidentally, I typed

> solveO(1113)
Error: evaluation nested too deeply: infinite recursion / options(expressions=)?

which shows R cannot handle heavy recursion without further programming. Testing for the upper limit, I found that the largest acceptable value is 555 (which takes forever to return a value, predicted at more than one hour by a linear regression on the run times till 300…).

Filed under: R, Statistics Tagged: Le Monde, mathematical puzzle, R, recursion

*Related*

To

**leave a comment** for the author, please follow the link and comment on his blog:

** Xi'an's Og » R**.

R-bloggers.com offers

**daily e-mail updates** about

R news and

tutorials on topics such as: visualization (

ggplot2,

Boxplots,

maps,

animation), programming (

RStudio,

Sweave,

LaTeX,

SQL,

Eclipse,

git,

hadoop,

Web Scraping) statistics (

regression,

PCA,

time series,

trading) and more...

If you got this far, why not

__subscribe for updates__ from the site? Choose your flavor:

e-mail,

twitter,

RSS, or

facebook...

**Tags:** Le Monde, mathematical puzzle, R, recursion, statistics