Maths Olympiad Prep

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Algebra Difficulty 6.0 AIME, harder Prove it Netherlands

Albert makes a sequence of numbers, the first 20232023 of which are exactly the numbers 11 through 20232023, in some order. To determine each subsequent number, Albert takes the median of the 20232023 previous numbers. You find the median of 20232023 numbers by sorting them by size and taking exactly the middle number from that sequence.
How many different values can the three thousandth number of Albert's sequence have?

Solution

1

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