Identifying Odd & Even Numbered Columns: D'Agapeyeff Cipher

In the last post I identified the mostly likely columns to have occupied even numbered positions in the original matrix:  C3, C7, C12, and C13.  I'm going to isolate these columns for purposes of this post.

As I referenced in a previous post, Friedman outlined a general solution for solving the ADFG(V)X cipher that relied on extrapolating data from cryptograms in the same key.  I'm going to use that same technique/assumption to try and tease out which three columns also belong in the same family.

If all four of these columns were even numbered in the original matrix, they should begin to show us a pattern of what the other even numbered columns look like by way of frequency counts.

  
If our assumption is correct, we can see a pattern emerging here.  The other even numbered columns should show few instances of 1 or 4.  Let's check the original matrix.  I've added counts for the other cipher numbers.

I want to first check the columns that have the next highest amounts of 3s.  C2, C4, C5, C6 and C10.

Of those five columns, one seems to fit the profile exactly:  C4.  It has only three instances of ciphertext 1 and ciphertext 4, while at the same time has six instances of ciphertext 2 and five instances of ciphertext 5.

The next most likely suspects are C6 and C14.  Not only do they have the fewest ciphertext 1s and ciphertext 4s (five each), they both have the next highest counts of ciphertext 2s (five each).

At this point, I feel comfortable moving forward to try and reconstruct the original pairs of columns.  But I'm a realist, I've only taken the possible transpositions from 14! or 87,178,291,200 down to 7! * 7! or 25,401,600.  So don't worry, I'm still daunted.