# Le Monde puzzle [#875]

**Xi'an's Og » R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

**I** learned something in R today thanks to Le Monde mathematical puzzle:

A two-player game consists in A picking a number n between 1 and 10 and B and A successively choosing and applying one of three transforms to the current value of n

n=n+1,n=3n,n=4n,

starting with B, until n is larger than 999. Which value(s) of n should A pick if both players act optimally?

**I**ndeed, I first tested the following R code

sole=function(n){ if (n>999){ return(TRUE) }else{ return((!sole(3*n))&(!sole(4*n))&(!sole(n+1))) }}

which did not work because of too many calls to sole:

>sole(1) Error: evaluation nested too deeply: infinite recursion / options(expressions=)?

So I included a memory in the calls to sole so that good and bad entries of n were saved for later calls:

visit=rep(-1,1000) #not yet visited sole=function(n){ if (n>999){ return(TRUE) }else{ if (visit[n]>-1){ return(visit[n]==1) }else{ visit[n]<<-((!sole(3*n))&(!sole(4*n))& (!sole(n+1))) return(visit[n]==1) }}}

**T**rying frontal attack

>sole(1) Error: evaluation nested too deeply: infinite recursion / options(expressions=)?

did not work, but one single intermediary was sufficient:

> sole(500) [1] FALSE > for (i in 1:10) + print(sole(i)) [1] FALSE [1] FALSE [1] FALSE [1] TRUE [1] FALSE [1] TRUE [1] FALSE [1] FALSE [1] FALSE [1] FALSE

which means that the only winning starters for A are n=4,6. If one wants the winning moves on top, a second counter can be introduced:

visit=best=rep(-1,1000) sole=function(n){ if (n>999){ return(TRUE) }else{ if (visit[n]>-1){ return(visit[n]==1) }else{ visit[n]<<-((!sole(3*n))&(!sole(4*n))& (!sole(n+1))) if (visit[n]==0) best[n]<<-max( 3*n*(sole(3*n)), 4*n*(sole(4*n)), (n+1)*(sole(n+1))) return(visit[n]==1) }}}

From which we can deduce the next values chosen by A or B as

> best[1:10] [1] 4 6 4 -1 6 -1 28 32 36 40

(where -1 means no winning choice is possible).

**N**ow, what is the R trick I learned from this toy problem? Simply the use of the double allocation symbol that allows to change global variables within functions. As visit and best in the latest function. (The function assign would have worked too.)

Filed under: Kids, R, Statistics, University life Tagged: assign(), global variable, Le Monde, local variable, mathematical puzzle

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

**Xi'an's Og » R**.

R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.