Le Monde puzzle [49]
Here is a quick-and-dirty solution to Le Monde puzzle posted a few days ago: the R code counts the number of winning tickets between 1 and N, and stops when there is a proportion of 10% of winning tickets.
#winning ticket win=function(n){ #decimal digits decomposition x=rep(0,4) x[4]=n%%10 m=(n-x[4])/10 x[3]=m%%10 m=(m-x[3])/10 x[2]=m%%10 m=(m-x[2])/10 x[1]=m%%10 tic=0 for (i in 1:3) tic=max(tic,(x[i]==1)*(x[(i+1):4]==3)) return(tic) } #number of winning tickets nwt=0 for (i in 1:9999){ nwt=nwt+win(i) if ((i>999)&&(10*nwt==i)) break()} #solution print(i)
The (only) solution is therefore N=3500. (I am using this home-made decomposition of a number into its decimal digits, but there must be some function doing that in R already!)
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Placing Digits in a Number into a Vector…
I enjoy reading about the Le Monde puzzles (and other topics!) at Christian Robert’s blog. Recently he asked how to convert a number with s digits into a numerical vector where each element of the vector contains the corresponding digit (by place valu…
December 7, 2010 at 4:08 pm
You could always use:
toDigits <- function(n){
x = as.character(n)
d =as.numeric(strsplit(x, "")[[1]])
lin = length(d)
return(c(rep(0, 4-lin), d))
}
Thanks for posting these!
Greg
December 7, 2010 at 9:13 pm
Thanks, Greg!