4. Median. In a set of 100 numbers. If one number is removed, the median of the remaining numbers is 78. If another number is removed, the median of the remaining numbers is 66. Find the median of the entire set.
Solution. Arrange the numbers in ascending order. If we remove a number from the first half of the sequence (with a number up to 50), the median of the remaining numbers will be the $51-\mathrm{st}$ number in the sequence. If we remove a number from the second half, the median of the remaining numbers will be the number with the 50th position, but it is not greater than the 51st number. Therefore, the 50th number is 66, and the 51st number is 78. Thus, the median of the entire set is ${ }^{2}$ $\frac{66+78}{2}=72$.

Answer: 72.[^1]