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I'm going with Chicago. Flagstaff has a better chance of having the last inch of snow in the spring. Flagstaff's snow is more winter/spring biased. Chicago's is straight on most likely in winter with fall and spring about equally likely. Seasonal lag puts Boston behind in the race. St. Louis is pretty unlikely, it's pretty far south. It could have a Hail Mary pass though.
As a rule of thumb, I'm going to say the day the daily likelihood of snowfall is 15% is about when the first inch is likely to arrive by.
I'd say that Chicago has about a 50% likelihood of being first, Flagstaff 40%, Boston 9%, and St. Louis 1%.
Chicago: November 13 (Usually their first inch is in November)
Boston: November 23
Flagstaff: November 16 (This one's pretty variable, it could easily be October or December)
St. Louis: December 19 (I have a feeling it will be earlier, maybe December 1-15)
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