Finite Mathematics

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. )

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

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.

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

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+.

Hi,

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

Cheers,
Wen Shih

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.