Finite Mathematics

• Forbiddensinner

  30 Jan 10, 10:05

  S = ( 1, 2, 3, ..., 20 )

  Determine the number of two-element subsets (a, b) such that a+b is a multiple of 4.

  Please share if you have a shortcut, thanks. ( And yes, I know how to add one by one, but that will be quite time-consuming. )

• wee_ws

  30 Jan 10, 14:59

  Hi,

    What is the smallest value of a + b, which is a multiple of 4?

    What is the largest value of a + b, which is a multiple of 4?

    For each multiple of 4, ask what a and b may be, so that the number of sets can be found.

    Try to observe a pattern on the number of sets.

    Thanks.

  Cheers,
  Wen Shih

• Forbiddensinner

  30 Jan 10, 19:40

  Originally posted by wee_ws:

  Hi,

    What is the smallest value of a + b, which is a multiple of 4?

    What is the largest value of a + b, which is a multiple of 4?

    For each multiple of 4, ask what a and b may be, so that the number of sets can be found.

    Try to observe a pattern on the number of sets.

    Thanks.

  Cheers,
  Wen Shih

  Sir, you are a genius.  Thanks a lot.

  Seriously, Number Theory is much more difficult, yet easier to score than Finite Maths.

• wee_ws

  1 Feb 10, 22:44

  Hi,

    Thanks. It's a matter of training after doing a gruelling course, haha :P

    Jiayou, and hone your investigative skills continuously to improve!

  Cheers,
  Wen Shih

• Forbiddensinner

  2 Feb 10, 16:21

  Originally posted by wee_ws:

  Hi,

    Thanks. It's a matter of training after doing a gruelling course, haha :P

    Jiayou, and hone your investigative skills continuously to improve!

  Cheers,
  Wen Shih

  Thank you Sir.

  I just failed my first number theory test. 

  There are so many zeroes around that it make me wonder if anybody actually pass it. 

  Okay, maybe Finite Maths will be easier to get A+. 

• wee_ws

  2 Feb 10, 16:27

  Hi,

    Acknowledge, forgive and learn from the mistakes. Have faith that you will do better next time. Jiayou.

  Cheers,
  Wen Shih

• Forbiddensinner

  2 Feb 10, 18:57

  Originally posted by wee_ws:

  Hi,

    Acknowledge, forgive and learn from the mistakes. Have faith that you will do better next time. Jiayou.

  Cheers,
  Wen Shih

  Thank you for the kind encouragement.

  I estimated that I have about 2.5% more margin for error before dropping from A+ to A.