Count subsets of finite positive integers constrained by sum

[Mohaimin]

You are given a set S of first 18 positive integers.
How many subsets of S will have sum greater than 85?

I was watching a video lecture on Symmetry. The problem was given in the booklet provided with the lecture. Its a hint

[sourav das]

$\sum_{i=1}^{18}i= 171$
now there are $2^{18}$ subsets of that set [as there are 2 options for every element]. [ note that we also count $\varnothing $ ]. Now denote the sum of the elements of a subset by $S$. So, For any subset $A$ with $0\leq S\leq 85$ we will get $A'$ for which $S$ is greater than 85.[As 0 to 85, there are 86 values and 86 to 171 also 86 values.]
So by symmetry there are $2^{18} / 2 = 2^{17}$ subsets like this.

[Mohaimin]

So by symmetry there are $2^{17} / 2 = 2^{16}$ subsets like this.

Everything is ok except this, I understand that it was a typing mistake

[sourav das]

Upps. Sorry.