Minus' Solution to

Perfect Piano Performance
Posted Weeks of June 1 - 14, 1998

Minus received so many wonderfully, prepared solutions that he's decided to forego his usual musings and let you be the stars. Without further delay, here are YOUR solutions to this challenge...

Yvette Tan and Kate Naude, of St.Hilda's Anglican School For Girls, delivered this whopper of a solution to our hungry mascot. Minus, as you can all predict, wolfed down this opening course in a blink of an eye.

We got our answer of 800 white keys, 500 black keys and 6 minutes and 40 seconds.

If Abner played 1300 notes in his piece and there were 26 keys altogether then he must have played the piano in an acsending order 50 times. This means he played each key 50 times.So what we did is multiply the 16 white keys by the magic number 50. This gave us our first answer which is 800 white keys.

If he played 800 white keys then he obviously played 500 black keys to get to the total answer of 1300. Our third and final answer is 6 minutes and 40 seconds because if he played 800 white keys at 0.5 seconds per key he took 400 seconds to play the 800 keys. Therefore 400 seconds divided by 60, because there are 60 seconds in one minute, is 6 minutes and 40 seconds.

Hello Minus, we found this problem quite simple- most likely because we are female...

One other thing before we start our solution- the wording of the questions "how many white/black keys were played" appeared like a trick question at first. The first answer that appeared to us were that of 16 and 10. Because every one of the notes was played and there were 16 of the white notes and 10 of the black ones. But enough of our pedantic criticism and onto the solution.

If there were 1300 notes played and only 26 notes then each note was played 50 times. So in answer to the questin of how many white notes were played it is simply 16*50 which is 800. There are 10 black notes so 10*50 is 500.  If each note was 1/2 second in length then 800 white notes would have taken 400 seconds to play which is equivalent to 6 minutes and 40 seconds.

summarised:
white keys = 800
black keys = 500
time taken to play white keys = 6 mins and 40 seconds.

Abner played through the whole keyboard 50 times. Therefore he played 800 white keys and 500 black keys. If he played 800 white keys taking 0.5 seconds per key then he took 400 seconds to play the white keys. That means that it took Abner 6 minutes and 40 seconds to play the white keys.

There were 800 white keys played, 500 black keys, and Abner spent 400 seconds playing the white keys.

1300 divided by 26 = 50.  He went through the keyboard 50 times.  Therefore, he played the white keys 50 times 16 = 800 times and  played the black keys 50 times 10 = 500 times.  800 times 0.5 = 400 seconds to play the white keys.

Abner played 800 white keys, 500 black keys, and spent 400 seconds (or 6 minutes; 40 seconds) playing white keys.  To figure out the white keys you divide 1300 notes by 26 keys.  The answer is 50.  Multiply 16 times 50.  It is 800.  To find out the black keys you multiply 10 times 50.

It is 500 (To check this add 800 and 500.  They equal 1300.).  To find out the time spent playing white keys you multiply 800 times .5 seconds.  It equals 400 seconds, or 6 minutes; 40 seconds.