Keyboards keys

Question

The keyboard of a piano has seven full octaves plus 2 extra white keys and one extra black key. There are 36 black keys on a piano. How many black keys are in one octave

Answer 1

1 octave = 8 notes, so 7*8=56

Therefore there are 59 keys on the keyboard.

59 - 36 = 23 white keys...

36/7 = 5 black keys per octave with a remainder of 1.

However, to accomodate the remainder, one of the 7 octaves

will have 6 black keys

5+5+5+5+5+5+6 = 36