12.2.64 Number theory
Condition: Find an odd two-digit number \( X \) that satisfies the following conditions: the sum of the digits of the number \( X \) is equal to \( Y \), the sum of the digits of the number \( Y \) is equal to \( Z \), and \( X+Y+Z=60 \). How many such numbers are there?
A huge number of interesting olympiad problems in number theory, and its various sections.