## Le Monde puzzle [#967]

**A** Sudoku-like Le Monde mathematical puzzle for a come-back (now that it competes with The Riddler!):

Does there exist a 3×3 grid with different and positive integer entries such that the sum of rows, columns, and both diagonals is a prime number? If there exist such grids, find the grid with the minimal sum?

**I **first downloaded the R package ** primes**. Then I checked if by any chance a small bound on the entries was sufficient:

cale<-function(seqe){ ros=apply(seqe,1,sum) cole=apply(seqe,2,sum) dyag=sum(diag(seqe)) dayg=sum(diag(seqe[3:1,1:3])) return(min(is_prime(c(ros,cole,dyag,dayg)))>0)}

Running the blind experiment

for (t in 1:1e6){ n=sample(9:1e2,1) if (cale(matrix(sample(n,9),3))) print(n)}

I got 10 as the minimal value of n. Trying with n=9 did not give any positive case. Running another blind experiment checking for the minimal sum led to the result

> A [,1] [,2] [,3] [1,] 8 3 6 [2,] 1 5 7 [3,] 2 11 4

with sum 47.

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