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I was wondering why it called a three-body problem (at least as it presented in Liu Cixin novel). There is actually at least 4 bodies (3 suns and a planet), right? I suppose the planet will affect the movement of the 3 suns.

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Probably a misnomer. And issue isn't really about the planet affecting the movement of the 3 suns (its mass can be considered deligible compared to them) but how the suns affect the movement of the planet. Essentially they're looking for a solution to the restricted 4bp rather the 3bp.

No, it's just three. The reason it's a thing – as far as I understand – is that solving analytically for one body is trivial: it's stationary. Solving analytically for two bodies is possible but takes some calculus. Three bodies have chaotic behaviour and need to be simulated.

in the novels there are 3 suns, so it is 4 bodies.

The simulation doesn't get easier with 4 tho, so 3 body problem is still a good name. Also the planets mass is "almost" negligible compared to that of the suns, so I assume simulating (+ occasional correcting) 3 bodies is already a good approximation.

It’s not a good approximation because (spoilers) the challenge is to identify the location of the planet relative to the suns, not simply to locate the suns themselves. I too wondered at the title.

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