[ Classical combinatorics (miscellaneous).] $[$ Inclusion-exclusion principle $]$

From the sequence of natural numbers, all numbers that are squares or cubes of integers have been erased. Which of the remaining numbers is in the hundredth place?
Let's consider the first hundred natural numbers. Among these numbers, there are ten squares (from 1 to $10^{2}=100$) and four cubes (from 1 to $4^{3}=64$). Note that two of these numbers, namely, 1 and 64, are both squares and cubes. Thus, from the first hundred, we have crossed out 12 numbers. Among the next twelve numbers, there are neither squares nor cubes ( $11^{2}=121,5^{3}=125$ ), therefore, among the remaining numbers, the hundredth place is occupied by the number 112.

## Answer

112.