She was playing by ear
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the answer to the riddle was "piano tuna"
In the Punchline Algebra book, page 13.2 likely contains a math problem or puzzle that needs to be solved. The question about why the piano didn't work is likely a joke or riddle included in the book to add humor and engage students. The answer to the math problem on page 13.2 would be related to the algebraic concepts being taught in that section, while the joke about the piano not working is a separate, unrelated element meant to lighten the mood.
For c major there are no sharps, for b flat major there are two flats, b flat and e flat
A note with a number (like C4) represents a note (C) in a particular octave (4th). A note without a number represents that note in any octave, and could be played in any octave. In the example, C4 represents "Middle C", or the 4th C up from the lowest C on a grand piano - 4 octaves above C0. A4 is the standard notation for a frequency of 440Hz.
C Natural is a whole step above B flat. If you look at a piano, a half step above B Flat is B Natural, and one more half step above that is C Natural. So it's a whole step from B Flat to C Natural.