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ocr_text: Okay, this is a classic decision theory problem, often called the "Secretary Problem" or a variation thereof.\nSince you can't go back and don't know the distribution of diamond sizes in advance, you need a strategy\nthat balances gathering information with the risk of discarding the best option.\nHere's the optimal strategy to maximize your probability of getting the largest diamond:\n1. Observation Phase: Decide on a number of floors to skip and only observe the diamonds. For 10\nfloors (N=10), the mathematically optimal number to skip is approximately Nje (where e = 2.718),\nwhich is about 10 / 2.718 = 3.68. Since you must skip an integer number of floors, the best strategy\ninvolves skipping the first 3 floors.\n+ So, you ride the elevator past floors 1, 2, and 3. As the doors open, you look at the diamonds but\ndo not take any of them, regardless of their size.\n+ Mentally note the size of the largest diamond you saw among these first 3 floors. Let's call this\nsize the "benchmark size".\n2. Selection Phase: Starting from floor 4:\n+ Look at the diamond on floor 4.\n+ Compare its size to the "benchmark size" (the largest from floors 1-3).\n+ If the diamond on floor 4 (or any subsequent floor) is larger than the benchmark size, take it\nimmediately. This is your choice, and the process stops.\n3. Final Floor Rule: If you reach floor 10 and haven't taken a diamond yet (meaning no diamond from\nfloor 4 through © was larger than the largest one you saw in the first 3 floors), you must take the\ndiamond on floor 10.\nWhy this works:\n«Skipping the first few floors allows you to establish a baseline or standard of comparison without\ncommitting too early.\n«If you skip too few (e.g., only floor 1), your baseline might be too low, causing you to pick a mediocre\ndiamond early on.\n+ If you skip too many (e.g., floors 1-9), the chance that the absolute largest diamond was among those\nyou skipped becomes too high, forcing you to take whatever is on floor 10.\n«Skipping roughly 1/e (about 37%) of the options gives the highest probability (around 37-40% for\nN=10) of selecting the single best option.\nThis strategy doesn't guarantee you'll get the largest diamond (no strategy can), but it mathematically\nmaximizes your chances of doing so.
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