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MathNet 2006 — Part 02 Question 42

Math Olympiad Vault · MathNet 2006 — Part 02

Question 42

On a blackboard Daniel wrote, from top to bottom, a list of positive integers less than or equal to $10$. Next to each number on Daniel's list, Martin wrote down the number of times that number appeared on Daniel's list, thus obtaining a list of the same length.

If you read Martin's list from the bottom up you get the same list of numbers that Daniel wrote from the top down. Find the maximum length that Daniel's list can have.