The "fun litle puzzle" was a nightmare to me when I first came across it, which was on the 1971 Putnam exam. I spent a lot of time trying to solve it by doing $2^x,3^x$. When Serge Lang told me after the test that  $2^x,3^x$ was a notorious open problem, I didn't know whether to be pleased that my intuition had led me to something widely held to be true, or annoyed that I had spent so much precious exam time on an approach that was doomed.

Anyway, solutions to problem 1 and other Putnam problems are available at various places on the net, in appropriate issues of the American Math Monthly, and in the three volumes of Putnm problems and solutions published by the MAA.

The "fun litle puzzle" was a nightmare to me when I first came across it, which was on the 1971 Putnam exam. I spent a lot of time trying to solve it by doing $2^x,3^x$. When Serge Lang told me after the test that  $2^x,3^x$ was a notorious open problem, I didn't know whether to be pleased that my intuition had led me to something widely held to be true, or annoyed that I had spent so much precious exam time on an approach that was doomed.

Anyway, solutions to problem 1 and other Putnam problems are available at various places on the net, in appropriate issues of the American Math Monthly, and in the three volumes of Putnam problems and solutions published by the MAA.