Before I venture a guess to your question (which sounds to me like a trick question!), I suggest you change the word "stone" to "substance," since I don't think gold qualifies as a stone; it's a precious metal. Now if the gold is ensconced within a stone or there is an obvious vein of gold throughout the stone, then no change would be needed.
That being said, the second student is not on the right track, because he is conflating exegesis and hermeneutics. While the two processes have certain commonalities and are not hermetically sealed off from one another, they do have their differences.
Whereas both processes reflect a mutual interest in words as to their cultural/historical denotations, connotations, syntax, grammar, etymology, and more, hermeneutics is more interested in what a passage means than in what it says, and exegesis on the other hand is more interested in what the passage says than in what it means. (Obviously, both exegesis and hermeneutics are both concerned with meaning, in a general sense, because meaning is the foundation of any attempt at "languaging," whether of the written/verbal, oral, and/or nonverbal types.)
The second student, then, has bypassed exegesis and has suggested a hermeneutic prematurely, without providing a clearly established link between what the writing says and what it means. He also hasn't given a rational reason why the type of stone cannot be known; he simply assumes that it can't. He gave up too soon, in my opinion.
The third student was obviously able to read the writing (I assume all three students have the ability to read this ancient Egyptian language), but he bypassed exegesis and went directly to hermeneutics, and along the way he engaged in eisegesis, meaning he imposed his meaning of precious onto the text and then acted on that understanding. Who knows, perhaps what was considered a precious stone in ancient Egypt was something other than a diamond.
Moreover, the third student may have been correct in his assumption that the stone must be a diamond, but can an exegete ever reach a level of absolute certainty? To do so would require he or she engage in time travel and confirm or disconfirm his or her theory of what an ancient text means by literally opening a door within the ancient setting to see what's on the other side of the door. The best an exegete can do is to 1) do his homework; and 2) see what happens when he shares his findings in the marketplace of ideas within his discipline.
The first student, to me, seems to be on the right track. First, she "argues" her case, which is critical in any exegesis. Language by its very nature can very often be ambiguous, and good exegesis provides with it reasons why a certain reading is preferable to a different or conflicting reading.
In a sense, rhetoric is the tool by which one makes his or her "case." One argues one's case and then gives someone else (a peer, for example) the chance to poke holes in it and perhaps come up with a better one. (Sorry, but this is the perspective through which I have been trained to see phenomena. "Facts," as good as they are, are a dime a dozen; how they fit into a cohesive theory or explanation for--in this case--what a writing says, requires rhetoric (i.e., persuasion), albeit a measured and suitably "scientific" one. After all, if you are going to persuade your teachers or peers of your reading of a text, you need to have done your homework. Then, as you lay out your findings in a socially approved way and within the framework of your discipline's accepted paradigms, you make your case. Rhetoric isn't just an adjunct to the process of reporting the findings of one's research; it is part and parcel of the process.)
So, did student number one do her homework? It would appear so, at least partly anyway. Her assumption that there may be an etymological link between kariptka and kariptko is perhaps warranted. However, the student needs to defend her choice of gold as the "precious stone," since it appears to have been based on no more than an etymological similarity between the two words. That similarity may not be enough to warrant her reading.
In conclusion, the second student gave up too soon and conflated exegesis and hermeneutics. The third student may have engaged in eisegesis, which is, of course, taboo. My vote, therefore, is for student number one. My vote is not without certain reservations, but of the three students she seems to have hewn the closest to some of the basic rules of exegesis. Her use of the words "must therefore be gold," however, begs to be proved.