A Cube of Resistors

Here is a puzzle for those of you with some knowledge of circuit analysis.

Imagine welding a cube of resistors, each resistor with the resistance of 1 Ohm. If you measured the resistance between opposite corners, what would it be?

Each black line represents a resistor of 1 Ohm. What is the equivalent resistance between the red points?
Each black line represents a resistor of 1 Ohm. What is the equivalent resistance between the red points?

Hints:

Do it the hard way: Distort the cube into a two-dimensional surface and use the full machinery of equivalent resistance (Y-Delta transformations, etc) to solve all the loops.

Do it the fun way: Think of the particular geometry of the cube, and its symmetries. Think of the fundamentals of circuit analysis. You really don’t need to calculate much if you know how to visualize the problem.

“The art of making love, muffled up in furs, in the open air, with the thermometer at Zero, is a Yankee invention.”
-President John Quincy Adams

Author: minustwofish

I am a quantum physicist.

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