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To get three eggs per day you would need at least 6 hens of a heavy laying variety like the Production Red. But you will need to understand that any chicken will lay very well in it's first year and possibly it's second year, after that the eggs will get larger but there won't be as many of them. Also after about a year of heavy laying when the hen is around 1-1/2 years old she will molt and while she is molting she will quit laying.
Also chickens lay according to the number of daylight hours that they receive, so in the dead of winter when the number of daylight hours is the shortest you will get fewer eggs, some hens will quit laying until spring. You can increase the egg production by providing artificial light to the hens by having a timer set to turn some lights on the the hen house and then turn off after they have been given the proper number of light hours for the time of year.
My hens are free range and only come into the hen house to roost at night so I get a batch of new chicks every year and band their legs with all the same color so I can keep a record of how old each group of hens are. Then through out the year I will take a hen from the oldest group here and there for a pot of Chicken and Dumplings, Noodle Soup, Gumbo or what ever recipe that I have that needs to cook for a long time. That way my oldest hens are always around 5 years old, there are always young ones to give me plenty of eggs and the hen house doesn't become over crowded.