15. (12 points) The teacher told Jia the hundreds digit of a three-digit perfect square, told Yi the tens digit, and told Bing the units digit, and informed them that their digits are all different. None of them knew the other two numbers, and they had the following conversation: Jia: I don't know what the perfect square is. Yi: I knew you wouldn't know. Bing: I already know what the number is. Jia: After hearing Bing's words, I also know what the number is. Yi: After hearing Jia's words, I also know what the number is. What is the number ( ) squared?
A. 14
B. 17
C. 28
D. 29
【Solution】Solution: First, list all three-digit perfect squares with no repeated digits.
\begin{tabular}{|l|l|l|}
\hline Hundred & Ten & Unit \\
\hline 1 & 6 & 9 \\
\hline 1 & 9 & 6 \\
\hline 2 & 5 & 6 \\
\hline 2 & 8 & 9 \\
\hline 3 & 2 & 4 \\
\hline 3 & 6 & 1 \\
\hline 5 & 2 & 9 \\
\hline 5 & 7 & 6 \\
\hline 6 & 2 & 5 \\
\hline 7 & 2 & 9 \\
\hline 7 & 8 & 4 \\
\hline
\end{tabular}
\begin{tabular}{|l|l|l|}
\hline 8 & 4 & 1 \\
\hline 9 & 6 & 1 \\
\hline
\end{tabular}
(1) According to the first statement of A, it excludes the cases of $625, 841, 961$.
(2) According to the first statement of B, B must not have $2, 4, 6$, leaving only $196, 256, 289, 576, 784$ (more importantly, at this moment, A and C do not know whether B knows the result, so they cannot further narrow down the range).
(3) According to C's statement, C must not have 6, otherwise, C would not know the result, thus excluding 196, 256, 576.
(4) According to A's second statement, A still does not know the result after the second statement, so A must be 2. A, due to C's statement, excluded 256, and thus knew that he was 289.
(5) The last statement is not useful, but it is a fact, because C does not know whether it is 289 or 784, and only after hearing A's previous statement can C know.

Therefore, this number is the square of 17.
So the answer is: $B$.