## Le Monde puzzle [#930]

**A** game Le Monde mathematical puzzle:

On a linear board of length 17, Alice and Bob set alternatively red and blue tokens. Two tokens of the same colour cannot sit next to one another. Devise a winning strategy for the first player.

**I**n the ‘Og tradition, this calls for a recurrent R code:

game=function(n=17,col=1,tak=rep(0,n)){ frei=rew=0*tak # stopping rule if (sum(tak==col)==0){ frei=(tak==0)}else{ for (i in (1:n)[tak!=-col]) frei[i]=(min(abs((1:n)[tak==col]-i))>1)} # left positions if (sum(frei)>0){ for (i in (1:n)[frei==1]){ prop=tak;prop[i]=col rew[i]=1-game(n=n,col=-col,tak=prop)}} # outcome of best choice return(max(rew))}

While I did not run the rudimentary recursive function for n=17, I got a zero return from n=2 till n=12, meaning that the starting player is always going to lose if the other player plays optimally.

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