Is it possible to eat in such a way that you'll never have to fart?

This is like the opposite of what they asked though. They didn't ask for healthy, they asked for less farting. Lots of vegetables will make lots of farting.

This. When I used to work a very physical job (2.5k+ Cal per day min) I never had flatulence. My diet was also better, but I ate a ton. Like so much food, but I guess that's what happens when you burn more calories in a day then most people do existing. I do not miss that job, I do miss my old body. It would be impossible to get that amount of exercise naturally.