So, a week of canned foods? Doesn't sound particularly cheap or healthy, but it meets your (arbitrary) requirements.
I think a far more interesting discussion is how to reduce waste streams, long term. Given that I haul my own trash to the dump every ~4 months in a trailer, I'm quite interested in this. Empirically, we don't produce much mass, just a lot of volume (filling an 8' trailer is only ~360lb of material, and I'd prefer to have that closer to 1000lb). So, 2.9lb/day for our house for a 4 month period, which includes some significant "construction waste" (moving the ferret room and getting rid of their old stuff).
Things I'm working on:
- Aluminum cans go to be recycled. The price is crap ($0.40/lb), but it's not taking up space that I need to haul.
- Tin cans are going to be recycled. I didn't do this last time, and they take up a lot of volume in the trash that could be put to better use.
- I need to crush milk jugs, because they're not getting crushed, and take up a depressing amount of volume for their space. You could use glass milk bottles and a milk delivery service, but... $$$$?
- Paper junk mail is a problem. Wow, is it a problem. That's a huge chunk of our trash volume. I'm considering shredding it to reduce the volume, but that's still going to the dump. I don't have a burner I can run it through, but I'm considering playing around with making paper logs out of it. Alternately, I could start sending back the business reply envelopes secured to a rock, but it's a lot of charities and that's kind of a dick move. Shredding it and putting it in the compost might work, but I need to research more on the inks used and what I can/can't safely run into the compost.
- Cardboard already goes to the shed for reuse, though I'm working on the details of the reuse. Possibly sheet mulching with grass.
I don't think a one week challenge is particularly useful, TBH. You can just defer the trash. Figuring out how to make a more long term reduction in the trash stream is of far greater value.