Check the NYSDOT reference markers (on state highways.) Columbia County is represented on the second line as county "81". You might be thinking of DMV regions.
A complete list (from memory, believe it or not!):
Region 1 Capital District/Eastern Adirondacks
11-Albany
12-Essex
13-Greene
14-Rensaleer
15-Saratoga
16-Schenectady
17-Warren
18-Washington
Region 2 Mohawk Valley/Western Adirondacks
21-Fulton
22-Hamilton
23-Herkimer
24-Madison
25-Montgomery
26-Oneida
Region 3 Syracuse/Eastern Finger Lakes
31-Cayuga
32-Cortland
33-Onondaga
34-Oswego
35-Seneca
36-Tompkins
Region 4 Rochester/Genesse/Western Finger Lakes
41-Genesse
42-Livingston
43-Monroe
44-Ontario
45-Orleans
46-Wyoming
47-Wayne*
Region 5 Buffalo/Niagara Frontier
51-Cattaragus
52-Chautauqua
53-Erie
54-Niagara
Region 6 Southern Tier
61-Allegany
62-Chemung
63-Schyler
64-Steuben
65-Tioga
66-Yates
Region 7 Watertown/North Country
71-Clinton
72-Franklin
73-Jefferson
74-Lewis
75-Saint Lawrence
Region 8 Hudson Valley
81-Columbia
82-Dutchess
83-Orange
84-Putnam
85-Rockland
86-Ulster
Region 9 Binghamton/Central/Western Catskills
91-Broome
92-Chenango
93-Delaware
94-Otsego
95-Schoharie
96-Sulivan
Region 10 Long Island
03-Nassau
07-Suffolk**
Region 11 New York City
X1-Bronx
X2-Kings
X4-New York
X5-Queens
X6-Richmond***
NOTES
*Wayne County used to part of Region 3, thus the slightly off alphabetical listing in Region 4.
**Long Island and New York City used to be a single region, 10, thus the missing numbers in each region.
***In NYC, the number 11 is represented by "X".
:-) Andrew