**Xi'an's Og » R**, and kindly contributed to R-bloggers)

**A** Le Monde mathematical puzzle in combinatorics:

Given a permutation σ of {1,…,5}, ifσ(1)=n, the n first values of σ are inverted. If the process is iterated until σ(1)=1, does this always happen and if so what is the maximal number of iterations? Solve the same question for the set {1,…,2014}.

**I** ran the following basic R code:

N=5 tm=0 for (i in 1:10^6){ sig=sample(1:N) #random permutation t=0;while (sig[1]>1){ n=sig[1] sig[1:n]=sig[n:1] t=t+1} tm=max(t,tm)}

obtaining 7 as the outcome. Here is the evolution of the maximum as a function of the number of terms in the set. If we push the regression to N=2014, the predicted value is around 600,000. .. Running a million simulations of the above only gets me to 23,871!A wee reflection lead me to conjecture that the maximum number of steps w_{N} should be satisfy w_{N}=w_{N-1}+N-2. However, the values resulting from the simulations do not grow as fast. Monte Carlo effect or true discrepancy?

Filed under: Books, Kids, R Tagged: Le Monde, mathematical puzzle, R

**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...