In The Great Gatsby, how long were Daisy and Gatsby together before he went to war?

The novel has a number of indicators which give us some
idea of how long Daisy and Jay were together, but there is a confusing
contradiction.

In chapter four, Jordan Baker tells Nick
about the occasion when she had first seen Daisy and Jay in each other's
company:

"When
I came opposite her house that morning her white roadster was beside the curb, and she
was sitting in it with a lieutenant I had never seen before. They were so engrossed in
each other that she didn’t see me until I was five feet
away."

The fact that they
were, "engrossed in each other" implies that they were in some sort of relationship
already. We can assume that this happened during Fall of
1917, since Jordan specifically mentions the event occurring in October
1917.

The next date she mentions is the
following year:

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"By the next year I
had a few beaux myself, and I began to play in tournaments, so I didn’t see Daisy very
often."

She adds
that:

"Wild
rumors were circulating about her — how her mother had found her packing her bag
one winter night to go to New York and say good-by to a
soldier who was going
overseas."

Based on the
above, we can assume that Jay and Daisy had been involved since fall of 1917 and parted
ways (when he left for the war) in the winter of 1918. This must mean that they had been
acquainted for at least three months -
October 1917 through to January 1918 (depending obviously, on the
specific dates). It could even have been four months. 

The
detail provided in chapter eight, however, contradicts what Jordan says. Jay had been
telling Nick about his relationship with Daisy and Nick mentions
that:

" ...he
took Daisy one still October night, took her because he had
no real right to touch her
hand."

In this, it is clear
that their relationship began in October. The contradiction
lies in what Nick says later:

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"On the last afternoon before he went abroad, he
sat with Daisy in his arms for a long, silent time. It was a cold fall
day,"

Also:

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"They had never been closer in
their month of love ,
...

This clearly suggests
that they had been together for a
month. 

F. Scott Fitzgerald might have
intentionally created this contrast to indicate the fragility of what we assume to know:
it is all a matter of perception and recall.