## Le Monde puzzle [#1061]

**A** griddy Le Monde mathematical puzzle:

*On a 4×5 regular grid, find how many nodes need to be turned on to see all 3×4 squares to have at least one active corner in case of one arbitrary node failing.*

*Repeat for a 7×9 grid.*

**T**he question is open to simulated annealing, as in the following R code:

n=3;m=4;np=n+1;mp=m+1 cvr=function(grue){ grud=grue obj=(max(grue)==0) for (i in (1:length(grue))[grue==1]){ grud[i]=0 obj=max(obj,max((1-grud[-1,-1])*(1-grud[-np,-mp])* (1-grud[-np,-1])*(1-grud[-1,-mp]))) grud[i]=1} obj=99*obj+sum(grue) return(obj)} dumban=function(grid,T=1e3,temp=1,beta=.99){ obj=bez=cvr(grid) sprk=grid for (t in 1:T){ grue=grid if (max(grue)==1){ grue[sample(rep((1:length(grid))[grid==1],2),1)]=0 }else{ grue[sample(1:(np*mp),np+mp)]=1} jbo=cvr(grue) if (bez>jbo){ bez=jbo;sprk=grue} if (log(runif(1))<(obj-jbo)/temp){ grid=grue;obj=cvr(grid)} temp=temp*beta } return(list(top=bez,sol=sprk))}

leading to

> dumban(grid,T=1e6,temp=100,beta=.9999) $top [1] 8 $sol [,1] [,2] [,3] [,4] [,5] [1,] 0 1 0 1 0 [2,] 0 1 0 1 0 [3,] 0 1 0 1 0 [4,] 0 1 0 1 0

which sounds like a potential winner.

July 20, 2018 at 8:15 am

[…] article was first published on R – Xi'an's Og, and kindly contributed to […]

July 20, 2018 at 7:45 am

[…] leave a comment for the author, please follow the link and comment on their blog: R – Xi'an's Og. R-bloggers.com offers daily e-mail updates about R news and tutorials on topics such as: Data […]