Curiosity aside:

Pooping happens when the body needs to eliminate undigested waste. Almost everything that is edible has some amount of indigestible material, but some has far less than others.

The other important factor is the stimulation of bile release. This usually happens in the presence of bitter foods: dark leafy greens, pickles and other fermented foods, ect. Fats are also known to stimulate bile release. Biles primary function actually is to break down fatty acids. Even if youve eaten mostly bio-available nutrients, if your gallbladder gets stimulated you could end up on the toilet anyway.

So if your goal is to avoid pooping for several days, your ideal diet will avoid fibrous and bitter fruits and vegetables, and avoid fatty foods.

If it were me, I would eat lean meats (chicken or venison), possibly dried into jerky, and simple fruits, or juiced vegetables and fruits. The less food you eat generally, the more you'll avoid building up waste in your intestines.

Just a heads-up: if your succeed in your goal and don't poop for several days, your first poop after can possibly be, erm, explosive. Your gallbladder will likely continue accumulating bile during your poop-fast, and the first thing you eat that stimulates it's release may flood your small intestines. So plan your first meal carefully!

God speed.