Adapted from reading "Algorithms" by Jeff Erickson
freely available on http://jeffe.cs.illinois.edu/teaching/algorithms/

n Queens Problem
Section2.1, page 69-71

Comparing to the wiki page on the "8 Queens Problem"
https://en.wikipedia.org/wiki/Eight_queens_puzzle
I can check that my implementation is finding the right number of solutions:

$ target/release/queens_problem 4 | wc -l       
2

$ target/release/queens_problem 8 | wc -l 
92

$ target/release/queens_problem 10 | wc -l 
724

$ target/release/queens_problem 12 | wc -l 
14200

$ target/release/queens_problem 14 | wc -l 
365596

That last run of 14x14 taking about 15 seconds to run on my AWS ec2:
$ time target/release/queens_problem 14 | tail -3 
[14, 12, 10, 8, 2, 5, 3, 1, 7, 11, 13, 6, 4, 9]
[14, 12, 10, 8, 2, 5, 3, 1, 9, 11, 13, 7, 4, 6]
[14, 12, 10, 8, 3, 5, 2, 11, 1, 6, 13, 9, 7, 4]

real    0m15.182s
user    0m13.734s
sys     0m5.616s

Also, try running with the "show" parameter, for instance:
$ target/release/queens_problem 4 show