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HMMT February

Combinatorics Difficulty 5.0 AIME Find the answer

What is the earliest row in which the number 2004 may appear?

A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.

Solution

By the previous problem, it cannot appear before row 12. By starting off the table as shown above, we see that row 12 is possible, so this is the answer.

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Source: Omni-MATH, licensed Apache-2.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.