"Excellence is not an act but a habit" - Aristotle
The page contains some math and logic problems that I have encountered over the years, that I enjoyed solving.

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 ?

Go here if you want the solution. 