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American Invitation Mathematics Examination. A 15 question test that is 3 hours long that is only given to those who score well enough on the AMC 10 or 12. Your AMC 10/12 score is used in combination with your AIME score to determine whether you qualify for USAMO or not. Unlike AMC 10/12, there is no multiple choice and the answer to each question is an integer from 000 to 999, inclusive. The first few questions are about the same difficulty as late AMC 10/12, but the difficulty ramps up as you progress further in the test.
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