In the United States we have a joke about chickens and eggs.  It is also a philosophical question.  Which came first, the chicken or the egg?  I remember my schoolmates debating this question and sixth grade.  “The chicken could not have come first because it grew out of an egg,” one student would say.  “But the chicken had to come first because something had to lay the egg,” another student would say.

So let me try to answer your questions.  Humans lay eggs without mating.  How can I say that?  Human eggs don’t have shells that a mature woman does produce mature eggs.  In the same way, a chicken produces eggs without mating.  The only difference is that chicken eggs have shells and are just a tad bit larger than human eggs (that’s an exaggeration.  Human eggs are microscopic.

An egg or a sperm is a gamete, and all gamete are 1n.  So how can some chicken eggs be 1n and other be 2n?  The answer is simple.  An unfertilized egg is 1n.  If there is a rooster around who manages to fertilize the egg he donates his gametes which are also 1n.  1n + 1n = 2n.  This creates a fertilized egg which is 2n, one set of chromosomes from the hen and one set from the rooster.  Because of your questions I’ll explain further in a moment.  But first let me answer other questions.

You’re correct when you say if the hens are separated from roosters they do not mate.  All their eggs will be unfertilized and so 1n.  In the same way, a human (man or woman) produces unfertilized eggs (women) or sperm (men) that are 1n.

Now that me explain the meaning of one set of gametes.  That term is incorrect.  I should have said one set of chromosomes.

Most adult animals, birds, fish, and so on, have two sets of chromosomes.  There are no male chromosomes or female chromosomes.  There are exceptions to almost every rule in biology and there are exceptions to these rules too.  In plants, especially, some individual plants are 3n, 4n, 8n, or even 16n.  Some amphibians and reptiles may be mature adults and be only 1n.  But those exceptions complicate the story considerably so I will ignore them for now.

Most of the cells in a person or a chicken are 2n.  On very rare occasions the chromosomes will not split properly and a person is born who is 3n or 4n, but that person is most likely sterile because they cannot produce viable gametes.

When eggs or sperm are created the cells divide differently than other cells.  In normal cells the two chromosomes double creating a cell with four sets of chromosomes.  This is the beginning of the process called mitosis.  In the process of mitosis that cell will divide into two cells each of which has the normal two sets of chromosomes.

When eggs or sperm are created the process is called meiosis.  A normal cell with two sets of chromosomes will have those chromosomes double creating a cell with four sets of chromosomes just like in mitosis.  Then something unusual happens in meiosis.  Instead of creating two cells with two sets of chromosomes the cell divides into four parts creating FOUR cells each of which has one set of chromosomes.  Just to be clear let me give you a short table.

One set of chromosomes = 1n (gamete)

Two sets of chromosomes = 2n (most cells)

Four sets of chromosomes = 4n (a cell in the process of mitosis or meiosis before it divides)

Eggs and sperm have only one set of chromosomes so they are 1n.  If a sperm (1n) meets an egg (1n) the cell membranes of both will create an opening so the chromosomes from the sperm can join the chromosomes of the egg and create a unique creature (2n).

Humans have 26 pairs of chromosomes.  Many things happened to those chromosomes.  But when egg and sperm are created each egg and sperm may get a different chromosome from the parent.  Human chromosomes have been assigned numbers.  So let’s say for chromosome 14 in a man you have chromosome 14A and 14B.  One sperm might get chromosome 14A while the next sperm might get chromosome 14 B.  That’s why brothers and sisters look quite different.  Let’s say one brother gets all chromosomes 1 to 26 in the A form.  Another brother would probably get about half of his chromosomes in the A form in the other half from the same parent in the B form.