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I think I might have partially asked this already in the comments on somebody else's question. As far as I remember it was in an anthology of four or five novella's or "long" short stories....I read it sometime in the 1970's but it might have been written earlier.

A woman is standing naked at a municipal swimming pool, no inhibition on nudity by any other users (everyone is nude) in this future society, she is actually flaunting her pregnancy and the fact she won the lottery to bear a child. The population is controlled by this measure and is referred to as winning a "Bingo Baby"

There's a few chapters on her life and marriage but then it is noticed a lot of other women are also pregnant but unlicensed, there is a race on to find what's going on, eventually an agent realizes that all the women have used the municipal swimming pools recently.

They track down clues about a rogue scientist who has been modifying his sperm to super-survive, he's been releasing it in pools all over North America.

That's all I remember, maybe then a manhunt but I'm not sure

Edit: I read this before I'd read any of Niven's Known Space books and I remember noting the similarity (about a lottery that allowed child bearing) when I finally got into Ringworld.

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    It's not by Larry Niven. I mention that because as soon as you mentioned the bit about winning a lottery, I remembered "the Fertility Lottery" was a plot device in some of Niven's "Known Space" stories. Earth's population was up to 30 billion and it was felt that this number should hold steady instead of being allowed to keep growing and growing. (Other human-colonized worlds did not feel the need for such restrictions, which may have been part of the UN's plan all along: "If people want to have large families, they will emigrate, and free up a little space for new babies to fill!") – Lorendiac Oct 12 at 15:22
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    But my point is that I believe I've read all of Niven's "Known Space" stuff at one time or another, and I don't remember anything resembling "the mad scientist has modified his sperm to get women pregnant in swimming pools in large numbers." So I'm just advising people to not bother trying to find that story among Niven's published works. It must have been someone else playing around with a similar premise about how things might work in an overpopulated future Earth. – Lorendiac Oct 12 at 15:24
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    Gives a whole new meaning to the term "pregnancy pool". – LSerni Oct 13 at 10:15

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