I don't believe anyone suggested that one *should *"write out the sequence" (it was a simple matter to *calculate *that the 25th term in the sequence would be 180°) and, clearly, the required sequence __did__ reach beyond that (25th) term!

Yes, I missed that fact that the actual (supposed) solution is beyond the 25th term. I was supposing that the OP had not actually found that solution, because there was no mention of that. And I probably didn't think carefully about what everyone had said, because I had just come back from a trip and was reading too fast. Or because I was focused on the confusion I mentioned about the meaning of "have 180°", which you also pointed out less directly than I did.

You are entirely right. The difficulty in the problem is precisely that,

**after **finding the "solution", one needs to think about the entire sequence in order to see that such a polygon is, at the least, questionable.

I can imagine some contexts in which one would accept a 180° angle in a polygon, though I didn't find any such explicit statements, though many just fail to mention it; definitions do vary (e.g. some allow self-intersection). What interests me more is how a polygon can have so many

**reflex angles** (making it very

**concave**, if not necessarily

**self-intersecting**).

On reading the problem yet again, though, I see that the angles forming the sequence do not have to be arranged in order (64, 68, 72, ...)

**consecutively **around the polygon, but might largely

**alternate **between large and small, which might help.

I left this unsent for some time to ponder whether the polygon can actually exist; I see that others have now discovered this issue, but appear to be assuming the sequence has to be in order. I don't intend to dig any deeper, as it is obvious that the author of the problem can't have intended anyone to actually visualize the "polygon".