16. (15 points) As shown in the figure, a "T" shaped frame can enclose 5 numbers on the August 2010 calendar. The sum of the 5 numbers in the two "T" shaped frames in the figure are 31 and 102, respectively. If a "T" shaped frame encloses 5 numbers in the following figure with a sum of 101, find the largest and smallest numbers among these 5 numbers.
【Solution】Solution: Let the middle number of the five numbers be $x$.
When the “ $T$ ” shaped frame moves down, the sum of the three numbers in the row is: $x+1+x+x-1=3 x$, and the sum of the two numbers in the column is $x+7+x+14=2 x+21$,
From this, we can derive the equation:
$$
\begin{aligned}
3 x+2 x+21 & =101 \\
5 x & =80 \\
x & =16 .
\end{aligned}
$$

At this time, the smallest number among the five numbers is $16-1=15$. The largest number is $16+14=30$.
Similarly, when the “ $T$ ” shaped frame moves up, we can derive the equation:
$$
\begin{array}{c}
3 x+2 x-21=101 \\
5 x=122, \\
x=24.4
\end{array}
$$

This does not meet the requirements of the problem;
When the “ $T$ ” shaped frame moves to the left, we can derive the equation:
$$
\begin{aligned}
3 x+2 x-3 & =101 \\
5 x & =104, \\
x & =20.8
\end{aligned}
$$

This does not meet the requirements of the problem.
When the “ $T$ ” shaped frame moves to the right, we can derive the equation:
$$
3 x+2 x+3=101
$$
$5 x=98$,
$$
x=19.6 \text {; }
$$

This does not meet the requirements of the problem.
Therefore, the largest number among these 5 numbers is 30 and the smallest number is 15.
Answer: The largest number among these 5 numbers is 30 and the smallest number is 15.