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Problem 471

AMC 12 late, AIME early

Number theory Difficulty 4.9 Find the answer

10.1. The numbers $1,2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}$ are written on the board. It is allowed to erase any two numbers and replace them with their difference - a non-negative number. Can the only number left on the board after several such operations be 17?

Your answer

Official solution

Answer: Yes, it can.

The desired sequence of operations is evident from the following record: 17 = $32-(16-(8-4-2-1))$ .

Note. An answer without specifying the sequence of operations - 0 points.

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.