This youtube video https://www.youtube.com/watch?v=GYFHMD_ja7c reveals a mathematical puzzle that had me fairly baffled, and for the time being I appear to disagree with the answer that’s proposed as distinctive.

A single sheet is torn off a e-book, and the sum of the web page numbers within the remaining sheets is 15000.
What is the sum of the web page numbers within the sheet that was torn off?

The ‘inevitable’ assumption I believe one must make, which can also be made within the video, is that pages are numbered with consecutive integers beginning at $1$ and ending at $N$ , with out skipping any quantity.
Unlike I beforehand thought, it’s not essential to assume that all sheets have numbers on each side.
However, if it is true that no numbers and no sheet sides are skipped from the numbering in between $1$ and $N$, it’s essential to assume that the solely attainable lacking web page numbers are the left facet one on the primary numbered web page (which might then begin at $1$ on its proper facet), or the best facet one on the final numbered web page (which might then finish at $N$ on its left facet).
If the torn off sheet had no numbering on both facet, no numbers can be subtracted from the sum, and, as proven later, that might be incompatible with the $15000$ determine.

I approached this puzzle in a barely completely different manner in comparison with the video.

Here is my answer (sorry, the hidden part formatting doesn’t appear to work with this, undecided why).

As talked about, $N$ is the final and highest web page quantity within the e-book, the primary and smallest being $1$.
If no sheet have been torn off, the sum of all web page numbers can be the identified formulation $frac {N(N+1)} 2$.
This expression can’t be equal to 15000 for any constructive integer $N$, thus the torn off web page will need to have at the least one web page quantity on it.

The sheet that’s torn off can’t be the primary or the final numbered one, both, no matter whether or not it’s numbered solely on one facet or each.
This might be proven by proving (e.g. numerically) that the next equation:
$frac {N(N+1)} 2 – S = 15000$
has no constructive integer answer for $N$ for any of the 4 talked about instances: $S = {1, 1+2, N-1+N, N}$.

Let $x$ be the quantity on the left facet of the sheet that’s torn off. As proven, that can not be the primary numbered sheet. Thus $x ge 2$.
$x+1$ is then the quantity on the best facet of the sheet that’s torn off. As proven, that can not be the final numbered sheet. Thus $x+1 le N-1$, i.e. $x le N-2$.

Once the sheet is torn off, $x+x+1$ is faraway from the sum, therefore:
$15000 = frac {N(N+1)} 2 – x – x – 1$
Solving for $x$:
$x = frac {N^2+N-30002} 4$

Applying the 2 boundary circumstances on $x$, i.e. $2 le x le N-2$.

$x ge 2$
$frac {N^2+N-30002} 4 ge 2$
Knowing that $N$ is a constructive integer, the one legitimate answer is:
$N ge 173$

$x le N-2$
$frac {N^2+N-30002} 4 ge N-2$
Knowing that $N$ is a constructive integer, the one legitimate answer is:
$N le 174$

So we all know that $N = 173$ or $N = 174$.

If $N = 173$:
$x = frac {N^2+N-30002} 4 = 25$
The sheet that’s torn off is the one numbered 25 on the left facet, 26 on the best facet.
This implies that all odd pages seem on left sides, all even pages on proper sides.
In flip, which means the final numbered sheet has $173$ on the left facet and isn’t numbered on the best facet.
The first numbered sheet as an alternative is numbered on each side, $1,2$.
All of that is per the hypotheses, there isn’t a contradiction, so this answer seems to be legitimate.

If $N = 174$:
$x = frac {N^2+N-30002} 4 = 112$
The web page that’s torn off is the one numbered 112 on the left facet, 113 on the best facet.
This implies that all even pages seem on left sides, all odd pages on proper sides.
In flip, which means the final numbered sheet has $174$ on the left facet and isn’t numbered on the best facet.
The first numbered sheet can also be numbered solely on one facet facet, the best one, with $1$.
Again, no contradiction with any of the hypotheses, so this answer seems to be legitimate, too.

Just to verify, I made an Excel sheet with the record of web page numbers and alternating left/proper labels, as per the 2 options, and eliminated in every case the suitable pair of consecutive pages: the sums are each $15000$.

First situation: is it OK to assign an issue that has two attainable options (assuming that just one is then scored as appropriate)?

Second situation: see 4:04 and 4:30 within the video.
In essence, solely answer $N = 173$ is taken into account legitimate, based mostly on the additional assumption that if a web page quantity is lacking, it may be essentially solely from the final web page.
My impression is that the video reaches just one answer as an impact of pointless assumptions.

Can you see any mistake in my reasoning?
Do you assume the answer proven by the video is the one legitimate one, or are each options certainly attainable, as I concluded, given the reasonably obscure (or say ‘open’) formulation of the issue?