"At the drop of a hat"?

Solution 1:

Since the earliest examples of this phrase in print have no specific mention of fighting, my bet is on the start-of-a-race explanation from James Rogers' Dictionary of Cliches:

DROP OF A HAT - Acting readily or on some single signal. In the 19th century it was occasionally the practice in the United States to signal the start of a fight or a race by dropping a hat or sweeping it downward while holding it in the hand. The quick response to the signal found its way into the language for any action that begins quickly without much need for prompting.

The earliest reference I could find was from a hearing on a bankruptcy law from an 1837 Register of Debates in Congress:

Solution 2:

From the Phrase finder:

: This saying is said to come from the American West, where the signal for a fight was often just the drop of a hat. It may have an Irish origin, based on something like "he's ready to fight at the drop of a hat" which in turn may be followed by "roll up your sleeves" or "take off your coat" ie items of clothing are involved in the start of fights.

Also, this might help:

: During the days of fairground boxing competitions, the public were invited to try their skill against the resident pugilist. In those days all men wore hats. In order to indicate willingness to enter the fray a man in the crowd would throw his hat into the ring. Since he was then bare-headed, he was easily identified as he made his way up to the ring.

Solution 3:

I see several websites claiming this expression is of Irish origin, alluding to the dropping of a hat as an invitation to fight, but I doubt this.

I think it's from dueling days. Conventionally the duelists would fire when a third party dropped a handkerchief. But I think it would often have been a hat.