#math trivia #237 solution

Answer:  16.  Similar to the solution to #236, there are at least two ways to count:

  • By a‘s, seeing how many c‘s yield a value of a+c that is square:
    • (a must be at least 1)
    • a = 1:  c = 0, 3, 8 (3 answers)
    • a = 2:  c = 2, 7 (2 answers)
    • a = 3:  c = 1, 6 (2 answers)
    • a = 4:  c = 0, 5 (2 answers)
    • a = 5:  c = 4 (1 answer)
    • a = 6:  c = 3 (1 answer)
    • a = 7:  c = 2 (1 answer)
    • a = 8:  c = 1, 8 (2 answers)
    • a = 9:  c = 0, 7 (2 answers)
  • By b‘s, seeing how many ways there are to represent b2 as a sum of digits:
    • b = 0:  none (a must be at least 1)
    • b = 1:  (ac) = (1, 0) (1 answer)
    • b = 2:  (a, c) = (1, 3), (2, 2), (3, 1) (3 answers)
    • b = 3:  (a, c) = (1, 8), (2, 7), …, (9, 0) (9 answers)
    • b = 4:  (a, c) = (7, 9), (8, 8), (9, 7) (3 answers)

Either way, there are 16 answers.

For the reader:  Show the result by counting a third way.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s