I am thinking of a three-digit natural number less than 200. If I round its triple to the hundreds, it increases by 36. Which number am I thinking of?

(M. Dillingerová)
Let the sought number be $x$. From the problem statement, we have the condition

$$
3 x+36=* 00
$$

where $*$ is one of the digits $4,5,6$. These values are given by the condition $100 \leqq x<200$. This can be rearranged to the form

$$
3 x=* 64
$$

where $*$ is one of the digits $3,4,5$. Given that the number $* 64$ must be divisible by 3, only the digit 5 is feasible. Now it is easy to calculate that the number I had in mind is 188.