To figure this problem, we first have to understand a few things. First there can only be six different numbers from 0-9. Second, A Latin table is like Sudoku so you can't have the same numbers in the same row or column. Third,the first digit can only be 1 because it is the only number when multiplied by 6 is still a 6 digit number.Fourth, the last digit has to be an odd number because even numbers will have repeating multiples.
With this we can solve the problem. Since Latin tables are like sudoku the same number can't be in the same row or column. since the first number must be one and the last number has to be odd we will have to find out where the 1 has to be in the last column. The number 1 has to be on the 3rd row because if it's on the second,fourth or sixth row the number will be even, if the number is on the fifth row the number will be 0 or five but if it's on the third row then it will work because 7x3 equals one.
From there we can work it out from right to left and top to bottom. The first column will be from top to bottom 7,4,1,8,5,2. The second last number has to be one of those numbers excluding 7 and 1. Through trial and error we will end up with 5 and the third last row will be 8 and the third row will be 2 and the second row will be 4. When we work all this out we end up with this solution.
A=1 B=4 C=2 D=8 E=5 F=7
N= 142857