5. (3 points) Given the rebus: MIMIMI + NYANYANYA = OLALAOY. Identical letters represent identical digits, different letters represent different digits. Find MI + NY.

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# Answer: 119

Solution: The rebus can be rewritten as OLAOLOY = (MI + NYA) $\cdot$10101. First, this means that the last digit of MI + NYA is Y. Second, if MI + NYA $<100$, the result will be a four-digit number. Let MI + NYA $=1 Z$ Y, where $Z$ is some digit.

Then OLAOLOY $=1 Z$ Y $0000+1 Z$ Y $00+1 Z$ Y. If Y $<9$, then the sixth and fourth digits of this number should match, but they do not match. Therefore, Y $=9$. Consequently, I + A $=9$. The digit $Z$ is actually $O$, which is 1. Therefore, MI + NYA $=119$.

An example exists: $848484+353535=1202019$.