It was quite a few months ago that you set up a musical puzzle that had quite a few mistakes in it. When you set up the musical scale upon the keyboard you inadvertantly forgot the flats and only used the sharps also the western uses of the scale are seemingly what you were asking to create. This leaves out many scales that are arabic, Japanese, Chinese, Persian etc. Major scales in western music are from any tone ABCDEFG and all can be flatted and sharped. The pattern is: tone whole step whole step half step whole step whole step whole step and a final half step. The minor scales (there are three types: natural, harmonic and melodic) are created upon the shifted whole and half steps starting on the sixth degree of the major scale it is then: tone whole step half step whole step whole step half step whole step whole step. Thus,the Natural minor scale named a minor is A B C D E F G A . To get the Harmonic minor, raise the seventh degree to G sharp. The Melodic minor raises the sixth and seventh degrees ( F sharp and G sharp) but this is only when going up the scale, when going down you use the un-raised or natural tones. You also overlooked the ancient Greek modes and the related scales such as the Locrian mode. One must not forget that all tones can be flatted and shaped, thus C major CAN be also thought of as B sharp major, D sharp=E flat E sharp=F etc. etc. this is the reason JS Bach wrote 24 parts to the Well Tempered Clavier-- and it was so amazing he wote a complete cycle in the 1740s So, you may wnat to research this and include as much of the truly usable and thus used scales but don't forget the pentatonic, whole tone, Neapolitan, Spanish and even more obscure but still used scales. Your original quiz was wonderfully thought provoking in a mathematical way but preposterous in a purely musical way and it ignores the history of music in a large way. Please look into this there are many books and many are easy to understand and there are some books of just scales and chords in musical staff that can clarify. Sorry to nit pick but minutiae in music is what my life is all about. Ole Bach wouldn't have it any otherway either! By the way, my e-mail is clavecin and that is French for HARPSICHORD. Hope all is well and hope to hear from you soon.