1. When does the market open?

Question

It opens every five days.

2. How often does the market open?
It opens every five days.

3. How many times does the market open?
It opens every five days.

(Which question is correct? Are all acceptable?)

Answer 1

#2 is correct.

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The answer to #1 should be a particular time of day or day of the year. Here are some examples:

It opens at 10:00 am each weekday.
It opens on October first and is open 8 hours a day for six months.

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An answer to #3 could be this: It opens once every five days.

Or you could rephrase the question:
How many times each week does the market open?
Answer: It opens at 10:00 am, five days a week.