1986 INMO

This was the first INMO conducted, it was conducted by the Indian Institute of Science, Department of Applied Mathematics

Problem 1

A person who left home between 4 p.m. and 5 p.m. returned between 5 p.m. and 6 p.m. and found that the hands of his watch had exchanged places. When did he go out ?

Problem 2

Solve:

\begin{cases} \log_{2} x + \log_{4} y + \log_{4} z = 2 \\[6pt] \log_{3} y + \log_{9} z + \log_{9} x = 2 \\[6pt] \log_{4} z + \log_{16} x + \log_{16} y = 2 \end{cases}