You walk into the Pythagorean theorem display of the Museum of Mathematics. To
one side is a portrait of Pythagoras on the wall. On the other is a simple right triangle,
displaying the three sides labeled a, b, and c. All along the hall, which encases this
display, are different proofs and examples, essays and geometric drawings. At the end of
the hall is a door with a ‘Do Not Enter’ sign. After looking around and not noticing
anyone watching, you quietly slip inside the room.
Before you is an odd-looking machine. At first glance it seems to look like just a pump
system of some sort. Many pipes and large containers fill the room, all connected to this
device. A few feet beyond the door is a control panel of sorts. You walk forward to get a
better look and notice that there are four large buttons on the panel. The first is red-
colored, with the letter ‘a’ engraved into its center. The second is a blue button, with the
letter ‘b’ standing out from the rest of it. The third is a magenta button, labeled ‘c’. The
fourth button is pure white and slightly set apart from the rest of the buttons.
Upon closer examination, the machine seems to make more sense. From the ceiling,
two wide pipes emerge. The pipe to the left is painted red, and the pipe to the right is
painted blue. A few feet below each of these pipes are what appear to be large, conical
filters. The bottom of each filter hangs over a single translucent vat. The vat is held in
the air by support beams on each side of it except the front. Connected to the bottom of
the vat is another filter. Below this filter is a much smaller container. This container is
appears to be translucent as well, and is secured to the ground.
Intrigued, you debate if you should mess with the machine or not. “What’s the worst
that could happen?” you say to yourself. Reaching out you press the red button marked
‘a’. A keyboard and small display screen pop up from behind the control panel. On the
