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Omni-MATH / We have n coins, one of which is fake, which differs in weight from the real ones and a two-pan scale which works correctly if the weights on the pans are different, but can show a…

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problem

We have nn{} coins, one of which is fake, which differs in weight from the real ones and a two-pan scale which works correctly if the weights on the pans are different, but can show any outcome if the weights on the pans are equal. For what nn{} can we determine which coin is fake and whether it is lighter or heavier than the real coins, in at most kk{} weightings?
Plain-text mathematical notation (without MathML)
We have n coins, one of which is fake, which differs in weight from the real ones and a two-pan scale which works correctly if the weights on the pans are different, but can show any outcome if the weights on the pans are equal. For what n can we determine which coin is fake and whether it is lighter or heavier than the real coins, in at most k weightings?
Original LaTeX notation
We have $n{}$ coins, one of which is fake, which differs in weight from the real ones and a two-pan scale which works correctly if the weights on the pans are different, but can show any outcome if the weights on the pans are equal. For what $n{}$ can we determine which coin is fake and whether it is lighter or heavier than the real coins, in at most $k{}$ weightings?

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Source and history

task_id
ffbeb7da-5fe3-5f3a-b2f9-f8e124c9f82f
task_key
test--ffbeb7da-5fe3-5f3a-b2f9-f8e124c9f82f
task_revision_id
1
config / split
/ test

Official source

initial import