"Excellence is not an act but a habit" - Aristotle

**The scales and the counterfeit coin.**- 1. This problem was given to me as a sort of challenge by my friends Heather
and Ross. You are given a bag of 117 coins of which 1 is a counterfeit.
This counterfeit is identical to the other coins except that it is slightly
heaver or lighter than the real coins. You are not told which. You are given
a set of precision balance scales, but no standard weights. You may use it
5 times. Can you isolate the counterfeit and how ?
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- 2. Find a solution for 118 coins and 5 weighings.
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- 3. Find a solution for 119 coins and 5 weighings.
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**The resistor cube**- This is an old problem; one that I encountered when I was in high school.
Nonetheless it can be a challenge if never seen before. Suppose that a group
of 12 1.0 ohm resistors make up the edges of a cube. They are connected at
the corners of the cube, and on opposite diagonal corners are input and output leads. What is the total resistance of the cube ?
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