I have submitted #1172 as a fix, which is a wholesale rewrite of the problem.

The underlying issue is that there are two ways to refer to the correct answer in a PopUp: you can enter the literal string for the correct answer as is done in this problem, or you can enter the index of the item in the array of choices. This becomes ambiguous when some of the choices in the PopUp coincide with indices of elements in the array. In such cases the default behaviour is to assume that the correct answer represents an index and not a string matching one of the choices.

In this question $popup3 has "0" listed as the correct answer. Since perl doesn't distinguish between strings and integers PG reads 0 to mean the index of the correct answer, so it sets the correct answer to be the 0th element of the array of choices, which is "?".

To get the desired behaviour here, add the noindex => 1 option to the end of $popup3 (it wouldn't hurt to add it to all of the PopUps). That forces PG to interpret the correct answer as being a string matching one of the choices and not an array index, so it will set "0" as the correct answer instead of the 0th element of the choices array.

Thanks so much for providing both an explanation of how to fix this (which I can use for other similar cases in the future) as well as a very nice rewrite of the problem. I lifted the rewrite just in time before the problem set opened. :-)

A small suggestion I have is to perhaps be explicit in the problem text that the expressions should be dragged to the box. I expect at least some students complaining that they never thought of this. Although there are plenty of UIs like this nowadays that it should be self-explanatory enough ...