# Le Monde puzzle [#869]

**Xi'an's Og » R**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

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**A** Le Monde mathematical puzzle once again in a Sudoku mode:

In annxntable, all integers between 1 and n appear n times. Ifmaxdenotes the maximum over the numbers of different integers on all rows and columns, what is the minimum value of max whenn=7? whenn=11?

**I** tried to solve it by the following R code (in a pre-breakfast mode in my Reykjavik Airbnb flat!):

#pseudoku n=7 T=10^4 vals=rep(1:n,n) minmax=n for (t in 1:T){ psudo=matrix(sample(vals),ncol=n) maxc=maxr=max(sapply(apply(psudo,1,unique),length)) if (maxcbut later realised that (a) the

sapply(apply(psudo,1,unique),length)failed when all rows or all columns had the same number of unique terms and (b) I did not have to run the whole matrix:

vals=rep(1:n,n) minmax=n for (t in 1:T){ psudo=matrix(sample(vals),ncol=n) maxc=max(length(unique(psudo[1,])),length(unique(psudo[,1]))) i=1 while((igaining a factor of 3 in the R execution. With this random exploration, the minimum value returned was 2,2,2,3,4,5,5,6,7,8 for n=2,3,4,5,6,7,8,9,10,11. Half-hearted simulating annealing during one of the sessions of AISTATS 2014 did not show any difference…

Filed under: Books, Kids, R, Statistics, University life Tagged: AISTATS 2014, Le Monde, mathematical puzzle, R, Reykjavik, sapply(), sudoku, unique()

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