Problem #PRU-100669

Problems Methods Invariants and semi-invariants Invariants

Problem

There are numbers $1, 2, 3, 4, 5, 6, 7, 8, 9$ and $10$ written on a board. Each time you make a “move” you can erase three of the remaining numbers, $a, b$ and $c$ , and replace them with the numbers $2 a + b$ , $2 b + c$ and $2 c + b$ . The goal is to make all the $10$ numbers left on the board equal. Is it possible?

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