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Omni-MATH / The numbers 2⁰,2¹,⋯,2¹⁵,2¹⁶=65536 are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one from the other, erase them both, and write the result…

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problem

The numbers 20,21,⋯,215,216=655362^{0}, 2^{1}, \cdots, 2^{15}, 2^{16}=65536 are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one from 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?
Plain-text mathematical notation (without MathML)
The numbers 2⁰,2¹,⋯,2¹⁵,2¹⁶=65536 are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one from 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?
Original LaTeX notation
The numbers $2^{0}, 2^{1}, \cdots, 2^{15}, 2^{16}=65536$ are written on a blackboard. You repeatedly take two numbers on the blackboard, subtract one from 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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Source and history

task_id
3656713e-51ec-5c77-bf0f-b02b5783c59e
task_key
test--3656713e-51ec-5c77-bf0f-b02b5783c59e
task_revision_id
1
config / split
/ test

Official source

initial import