The Great CFC Low Income Food Experiment Challenge!

[dutchfire]

If you have a car and don't mind eating the same things over and over than, yes, it is possible. The big problem is really poor people don't have cars and so are stuck either buying from corner stores in the ghetto who typically have poor selection and high prices or to confine themselves to what they can carry on a bus trip which, once again, limits the ability to shop around for the lowest price and takes a heavy toll on the amount of time which must be spent traveling. The other problem is to get the lowest prices you often have to buy in bulk but to keep to the $20 limit you can't do that so you're stuck buying smaller packages at higher per unit prices.

Can it be done? Sure, but it will be tight, you'll end up eating a lot of the same stuff over and over, and without that variety no it won't be nutritious over the long term.

Food deserts are a thing, I know, but at least most European cities will have decent to good supermarkets available within walking/cycling distance. Also, assuming you are healthy and somewhat fit, and have a backpack, you can carry quite a lot in one go.
Buying in bulk is cheaper, but it's not like you are buying for hundreds of euros in one go. Just buying €2 worth of pasta can serve you for quite some time. I think the only item where buying real big is useful is rice, but even then you're only buying €10-€20 at a time.

Basically, there are quite a lot of additional problems someone might have (health issues which require specific food, living in an area with poor shopping opportunities, not having cooking equipment, storage space etc.), but this thread wasn't to address that. It just asked the basic question, can one eat for €20 a week. I'd say the answer is yes, but it is pretty tight and requires you to almost exclusively eat 'the optimal things'.

 

[Patroklos]

I think food allergies would be a bit issue to a lot of people. Gluten intolerance too.

However, that is not a particularly large swath of the people in general including the poor.