Quote from: TeQuiero on September 20, 2018, 05:44:03 AM

Quote from: r1s2g3 on September 20, 2018, 04:50:52 AM

Now we start with 2¹⁴ i.e 16384 and check how many merits it can generate.
16384 + 8192 + 4096 + 2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1 = 32767

Your topic reminds me of the old days in high school. Smerits are generated like radioactive decay and above sum is a geometric progression
I still remember that there's a general method to calculate this sum:

Assume that S = 16384 + 8192 + 4096 + 2048 +1024 + 512 + 256 + 128 + 64 +32 + 16 + 8 + 4 + 2 + 1
= 2¹⁴ + 2¹³ + 2¹² + ... + 2¹ +2⁰ (*)
then 2S = 2¹⁵ + 2¹⁴ + 2¹³ + ... +2² +2¹ (**)

(**) - (*) side by side, then S = 2¹⁵-1 = 32767

Btw, it's an interesting discovery OP.

I know, I can directly use the formula, but I just wanted it to be in laymen terms, where everybody can visualize each divison and the sum.

I like the analogy of sMerits vs radioactive decay but only difference is that they do not produce any unwanted product (like radiations)