Enigma 1428: Foursight
From New Scientist #2589, 3rd February 2007
If you place a 1, 2, 3 or 4 in each of the sixteen places in a 4 × 4 grid, with no digit repeated in any row or column, then you end up with a “Latin square”. Then you can read eight four-figure numbers in the grid, namely across each of the four rows and down each of the four columns.
Your task today is to construct such a Latin square in which those eight numbers are all different, none is a prime, no two are reverses of each other, and:
(1st column × 3rd column) ÷ (2nd row × 3rd row) > 4
What is your Latin square?