The minimum number of comparisons required to find the minimum and the maximum of 100 numbers is _________.

To find both the minimum and the maximum of $n$ numbers simultaneously using the optimal pairwise comparison method:

1. If $n$ is even, compare the first two elements to initialize the current minimum and maximum (requires $1$ comparison).

2. For the remaining $n - 2$ elements, process them in pairs:

   • Compare the two elements in the pair ($1$ comparison).

   • Compare the smaller element with the current minimum ($1$ comparison).

   • Compare the larger element with the current maximum ($1$ comparison).

   This takes $3$ comparisons for every pair, giving $\frac{3}{2}(n - 2)$ comparisons.

3. Total comparisons formula for even $n$:

   $$\text{Total comparisons} = 1 + \frac{3}{2}(n - 2) = \frac{3n}{2} - 2$$

4. Substituting $n = 100$:

   $$\text{Total comparisons} = \frac{3(100)}{2} - 2 = 150 - 2 = 148$$

Thus, the minimum number of comparisons is 148.