Final answer:
The 3 carat brilliant cut red diamond is likely the most valuable due to its rarity and unique color. The 3 carat F1 quality colorless diamond and 3 carat fancy yellow diamond are valuable but less so compared to the red diamond. The value of the 6 carat uncut diamond would need further evaluation after cutting.
Step-by-step explanation:
Among the diamonds listed, the 3 carat brilliant cut red diamond would likely be the most valuable. The value of a diamond is determined by a combination of factors known as the 4Cs: Carat, Cut, Color, and Clarity. This particular red diamond stands out due to its rare color. While colorless diamonds are valuable with grades like D being the highest for colorless stones, colored diamonds, especially red ones, are exceedingly rare and highly sought after, often commanding higher prices.
The F1 quality emerald cut colorless "D" diamond is also valuable due to its clear, colorless quality and high-grade cut. Nonetheless, it is outmatched by the rarity of the red brilliant cut diamond. The "fancy yellow" I3 diamond has lower clarity and while its yellow color does add to its value, it does not typically reach the value of rare red diamonds. As for the uncut 6 carat colorless diamond, it has potential value but would need to be cut and further evaluated for its clarity, cut quality, and color after cutting to truly assess its worth.
Gem treatments like irradiation or oil and epoxy treatments may enhance color but should always be disclosed, as non-disclosure can lead to a situation of asymmetric information, disadvantaging buyers. Hence, whether a gemstone has been treated can also significantly influence its value.