If you need to walk around a lot, it'll be tougher to do it on am empty stomach, but not impossible. You have plenty of energy stores to last 3 days unless you're significantly underweight to start with.
You will not be able to eat your daily allowance of calories for three days and not need to poop during that time. It's just not a thing that's going to happen for you.
If you are determined to eat and not poop, eat protein bars, and take an anti diahrreal (e.g., Imodium). You won't poop, but day 4-5 will be awful.
Realistically, if you eat anything, you'll poop. Tail down your calorie intake to ~1000 calories at day -7, to -500 on days -6 and -5, then to 0 for days -4 through -1. Start eating again on day zero.
You won't have to poop during that time. Make sure to drink water, and i would add electrolytes to ensure you don't get any type of heart arrhythmia (unlikely on a fast this short, but intelligent anyway).
I don't know why you need to do this, but good luck. I've done week long fasts before and they're not too hard after the first couple of days. Ironically, eating well before the start makes it MUCH harder (you'd think it'd tide you over, but it just makes your body expect food) ... Hence, the tailing down over a couple days.
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