MathDB
2014 Guts #8: Numbers on Blackboard

Source:

February 25, 2014

Problem Statement

The numbers 20,21,…,215,216=655362^0, 2^1, \dots , 2{}^1{}^5, 2{}^1{}^6 = 65536 are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one form the other, erase them both, and write the result of the subtraction on the blackboard. What is the largest possible number that can remain on the blackboard when there is only one number left?
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