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**F**ollowing the presentation of the first *Le Monde* puzzle of the year, I tried a simulated annealing solution on an early morning in my hotel room. Here is the R code, which is unfortunately too rudimentary and too slow to be able to tackle *n=1000*.

#minimise sum_{i=1}^I x_i #for 1le x_ile 2n+1, 1e ile I # Ige n, x_i ne x_j # a=x_i,b=x_j,i,jin I implies a+b=x_k for a kin I n=6 m=2*n+1 complete=function(inde){ len=length(inde) comp=outer(inde,inde,"+") diag(comp)=inde comp=sort(unique(comp[complen)&&(length(comp) n){ off=sample(ind,1,prob=ind) newinde=sort(ind[ind!=off]) newinde=complete(newinde) if (tempe*log(runif(1))

The solution to the puzzle (given in the nextLe Mondeissue) is to take only the even digits, resulting in a minimum sum equal ton(n+1).Filed under: R, Statistics Tagged: Le Monde, mathematical puzzle, simulated annealing

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