Puzzles and logic › Processes, invariants and strategy › Board operations and invariants

Final number from repeated operation

High school · ●●●○○ 50 pts

The 97 numbers 491,492,493,…,4997\frac{49}{1}, \frac{49}{2}, \frac{49}{3}, \ldots, \frac{49}{97} are written on a blackboard. Repeatedly pick two numbers a,ba, b on the board and replace them by 2ab−a−b+12ab - a - b + 1 until only one number remains. Find the final number.

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