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When Were Holden's Madman Days?

Most Likely: December 1949

The madman days were right before the Christmas holidays, so it is December. But what year?

Holden was 16 during his madman days (p. 9). He turned 17 by the time he writes the story, which is sometime before the next September (p. 1, 9, 214). This means that he had a birthday as early as January (or even late December) and before September. 
Jan                 July     Sept      Dec
------------------------------------------
|========birthday===========|
We also know that when his brother Allie died, on 18 July 1946, Holden was 13 (p. 38). Therefore, Holden was 16 on 18 July 1949: exactly three years after Allie's death. But is he still 16 when December 1949 rolls around, or has he turned 17 by then (sometime before September), making the story take place the previous December (1948)?
Since there is twice as much time between January (late December) and July than there is between July and September, it's more likely his birthday is between January/late December and July. This means that Holden's madman days were most likely in December of 1949.

(The Catcher in the Rye was published in 1951.)