Xi'an's Og

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:

[sourcecode language=”r” gutter=”false”]
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)}
[/sourcecode]

Running the blind experiment

[sourcecode language=”r” gutter=”false”]
for (t in 1:1e6){
n=sample(9:1e2,1)
if (cale(matrix(sample(n,9),3))) print(n)}
[/sourcecode]

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

[sourcecode language=”r” gutter=”false”]
> A
[,1] [,2] [,3]
[1,] 8 3 6
[2,] 1 5 7
[3,] 2 11 4
[/sourcecode]

with sum 47.

This entry was posted on September 30, 2016 at 12:16 am and is filed under Books, Kids, pictures, Statistics, Travel, University life with tags arithmetics, Le Monde, mathematical puzzle, prime number, primes, R, R package, sudoku. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.