Le Monde puzzle [1]
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Following 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 next Le Monde issue) is to take only the even digits, resulting in a minimum sum equal to n(n+1).
Filed under: R, Statistics Tagged: Le Monde, mathematical puzzle, simulated annealing
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