Little math problems September 2018

[ijabbott]

Balls!

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The puzzle with the balls has a degenerate case. Suppose that all pairs picked are matching
pairs until the box is left with only an unmatched pair. This must be removed on the next pick and
replaced with a single black ball. Therefore, the remaining ball is black.

Sometimes if you know the puzzle has a single answer, it is easier to consider the simplest way to get to that answer, rather than consider all ways of getting to the answer. Like with the "remaining volume of a sphere with a six inch tall cylinder cut through the centre" puzzle, you know it has a single answer, and the simplest way of getting to the answer is to consider the degenerate case.