The number of multiples of $3$ more than $100$ but less than $700$.

Question

hartnn · Answer

floor(700/3)-floor(100/3)

parthkohli · Answer

So I can just subtract $100$ to get this expression: The number of multiples of $3$ more than $0$ but less than $600$. So will $\lfloor 600/3\rfloor$ work too?

hartnn · Answer

no, i don't think so...

hartnn · Answer

counter example :
no. of integers greater than 21 but less than 24

hartnn · Answer

*multiples of 3

hartnn · Answer

actually answer = 0, if you do 24-21 , you get 1

hartnn · Answer

with floor(24/3)-floor(21/3) also you get 1 :P

hartnn · Answer

i think you should add 'more than or ='
instead of just 'more than' for that formula to work.

parthkohli · Answer

Okay :)

parthkohli · Answer

Oh, I got why it does that =)

parthkohli · Answer

I can just subtract $1$ if the base case is a multiple of $3$ right?

parthkohli · Answer

(if I am using "more than").

hartnn · Answer

but for your original Q , you don't need to subtract 1
floor(700/3)-floor(100/3) is correct....

parthkohli · Answer

Yes because the base case is not a multiple of $3$. =)

hartnn · Answer

oh, you mean if numbers are multiples of 3....
yes, then subtract 1

parthkohli · Answer

Yeah, the numbers that we start and end with.
If only one is a multiple of $3$, subtract $1$. If both, $2$.
Gotcha!

hartnn · Answer

if both subtract 2 ??? 
see my counter example
both---->but subtract 1 only.

hartnn · Answer

If only one/none is a multiple of 3, subtract 0. If both, 1.

parthkohli · Answer

Oh yes