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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!)
Filed under: R, Statistics Tagged: Le Monde, mathematical puzzle, R
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