Back in high school, when I was heavily preparing for the AMC 10 and 12, I would thoroughly analyze past problems. I constantly reworked the tricky ones to engrave the techniques, shortcuts, and core motivations behind the solutions found in the Art of Problem Solving (AoPS) textbooks. But what always fascinated—and frustrated—me was that no matter how much I prepared, certain types of problems never appeared in those textbooks. They defied standard categorization; they weren't strictly algebra, geometry, combinatorics, or number theory.
For instance, the AMC would occasionally define a bizarre, made-up game and ask a complex question regarding the optimal winning strategy or the number of possible outcomes. Other times, it would be a logic puzzle—not the simple kind you find in elementary school puzzle books, but something genuinely tricky and layered. Because I never had enough exposure to these unconventional problems during the year, I would often end up successfully solving highly advanced problems in the final five questions, only to completely miss a strange "troll" problem in the first ten. Even if I carefully analyzed one of these game problems after the contest, I would still freeze up when a brand new one appeared the following year. If I hadn’t struggled with this specific blind spot, I would have been much more confident on test day and could have easily achieved the Distinguished Honor Roll.
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