Question 68
Albert makes a sequence of numbers, the first $2023$ of which are exactly the numbers $1$ through $2023$, in some order. To determine each subsequent number, Albert takes the *median* of the $2023$ previous numbers. You find the median of $2023$ 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?
How many different values can the three thousandth number of Albert's sequence have?