Use the box cutter to remove the bottom 9 inches of both soda bottles. Discard the bottoms. Remove the bottle lids. In one of the lids, carefully cut a star shaped hole out using the box cutter. In the second lid, use the thumbtack to poke a tiny hole right in the middle. Screw back on the lids. Stuff the cheesecloth into the neck of the bottle with the tiny hole.
Place the coffee grounds into the large paper filter and fold in the sides. Place in the bottle with the star-shaped hole, open side-up. Place on top of the pitcher and set this apparatus on top of a digital scale. Tare the scale, the slowly pour the water in a spiral over the grounds to bloom the coffee. This step should take about 30 seconds. Top with the small coffee filter.
Nestle the bottle with the cheesecloth on top of the coffee-filled bottle. If the setup is wobbly, use the rubber bands to secure the chopsticks or rulers as braces on the sides of the bottles.
Tare the scale again and weigh the ice into the top of the rig; it should sit on top of the cheesecloth. Place the rig out of direct sunlight and let slowly brew until all of the ice has melted and passed through the coffee, 10 to 12 hours. If you’re keeping an eye on the coffee brewing process, you should see one drop of water moving through the coffee about every 7 seconds.
Once the coffee isdone brewing, remove the rig from the pitcher and discard or compost the coffee grounds. Serve immediately over ice or transfer to an airtight container and refrigerate for up to 1 week.