How can 4 couples arrange themselves around a table so that each person is next to their spouse and a person of the same gender ?

Round table.
WA, HA, HB, WB, WC, HC,HD,WD

W=wife. H=husband

Yes like @chyna said. Works perfectly.
male male female female male male female female.
Of course there are only options in the choice of male or female of each couple.

Rectangle table:
Top of picture :one side left to right” Man Women,Man /Women
End of table right side: Women
Bottom of picture of table: End of table left side : Man
Bottom of pictue of rectangle table: Women.Man/Women.Man

Gender fluidity.

That would make for a boring dinner party. To keep the conversation going, no one should be sitting next to a spouse, and have someone of the opposite gender sitting on both sides.

It seems to me that these arangements could also be the basis of pairing off at various swingers parties.

You know gender is just a social construct right?

I’ve been to dinner parties like @zenvelo describes and those are the best. Nobody is next to their spouse. I’ve been to dinner parties where the seats are switched between the appetizer, the entree and dessert and those were fun, too (again, with nobody next to their spouse or date).

Interesting social commentary, but there is a math problem here as well. How many ways can we arrange these people? It turns out there are only 6 such arrangements. Here is the reasoning.

Number the seats going clockwise 1 to 6. We can always place the women in seats 1,2, 5 and 6, rotating the table if necessary. We notice that once the women are in place, the positions of their husbands is determined, so we just need to count the number of ways of arranging the women. A little less obvious is that we can always place woman 1 in seat 1. But what if, for example, the arrangement starts 2,1? We notice that in that case, the counter-clockwise arrangement starts 1,2, so there is a corresponding clockwise arrangement, the only difference being that the people to a person’s left and right swap places, but everyone is still next to the same people.

With woman 1 ensconced in seat 1, there are 3 women who can be next to her and 2 ways of arranging the other two women in seats 5 and 6. That makes for 3×2 = 6 arrangements, as listed below. Husbands of the wives 1, 2, 3 and 4 are 1’, 2’, 3’ and 4’

1,2,2’,3’,3,4,4’,1’
1,2,2’,4’,4,3,3’,1’
1,3,3’,2’,2,4,4’,1’
1,3,3’,4’,4,2,2’,1’
1,4,4’,2’,2,3,3’,1’
1,4,4’,3’,3,2,2’,1’

Being left-handed, it is preferred to sit in the far left-hand seat at the table or an end.

This is math so….I’m out :(

Have everyone sit ON the table in a circle. They will then be NEXT to EVERYONE!

Let’s just eat. We can play Jr. Math Club later. Maybe after Pictionary.

Step 1: Admit you’re gay.
Step 2: Marry your same sex partner.
Step 3 : Have the neighbors over for an orgy and tear up the seating chart.

Looks like all of the combinations are mentioned.

I think it’s best not to sit next to your spouse also, but even if you do, you have the person on the other side and across from you if it’s a rectangular table. If it’s a circle you really only have the people on either side assuming it’s a 60 inch table, especially if the room has a lot of background noise. If you are at a 72 inch, which can actually hold ten, but Can be used for either, then other people are really at a distance except the people next to you.

I saw a show that at White House parties it’s typical to not sit next to your spouse. I don’t know how true this is. Supposedly, they put a lot of thought into who sits next to who, that I believe, and meeting new people is expected.

I did table assignments at my wedding and I wish I hadn’t, although one set of friends met at my wedding, seated next to each other, and the married couple introduced my single friend to a friend of theirs, and they have been together since then, almost 30 years.

In coming up with this problem, I was not trying to create an ideal seating arrangement. I imagined what would happen if everyone was so jealous of their spouse that they needed to sit next to each other and not have their spouse sit next to anyone of the opposite sex. It was initially unclear if such a seating arrangement was even possible and after seeing it, how atypical it appeared. We seem to be so familiar with the pattern: boy, girl, boy, girl,...

They can sit on each others laps.