Problem for you #2: Let's see who solves this first.
[x] + [x+1/3] + [x + 2/3] - 3x + 15 = f(x)
Find the fundamental period of f(x) if it is periodic.
WHERE [ ] IS THE GREATEST INTEGER FUNCTION.Or The floor function. Or the integral part of x.

Question

Problem for you #2: Let's see who solves this first.
[x] + [x+1/3] + [x + 2/3] - 3x + 15 = f(x)
Find the fundamental period of f(x) if it is periodic.
WHERE [ ] IS THE GREATEST INTEGER FUNCTION.Or The floor function. Or the integral part of x.

experimentx · Answer

1/3??

anonymous · Answer

Yeah. Whats the method?

experimentx · Answer

analyze [x] + [x+1/3] + [x + 2/3] between 0 and 1

anonymous · Answer

Why between 0 and 1?

experimentx · Answer

because 0 is my favoraite no ... seems to simplify things a lot
15-3x is a linear function decreasing continuously, and it seem to give integer values for multiple of 1/3
also addition of multiple of 1/3 to x in floor seem to give integer ... between interval 0 and 1/3 it seem to decrease ... and suddenly at 1/3 it would jump ... and same pattern would repeat on 2/3

experimentx · Answer

let's say my answer is more observational than mathematical

experimentx · Answer

i tried to prove 
[x + L] + [x +L +1/3] + [x +L + 2/3] - 3L  = [x] + [x+1/3] + [x + 2/3]
this seems true only for 1/3 ... though i can't find algebra for it

experimentx · Answer

can you show me yours??