The integer part of n/2

Sdagg wrote: The integer part of n/2 I get integer part of (n+1)/2 Can you show your working?

I get the answer is $2$. Just take $n$ and $n-2$, we'll get $n-1$. Then, take both $n-1$, we'll get $n-1$. After that, take $n-1$ and $n-3$, we'll get $n-2$. Then $n-2$ and $n-4$, we'll get $n-3$, and so on until we take $1$ and $3$, we'll get $2$. (Correct me if i'm wrong)

The answer is 2. 1 is not possible since it is the smallest number(it does not lie between any two numbers, the mean of two numbers lies in between of both the number) and at any point we can't obtain a smaller number than 1 because the smallest possible mean is (2+3)/2 = 5/2 > 1. Hence, we check for 2. Obtaining 2 is possible for all n. Construction of above post demonstrates this.