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Omni-MATH / The time on a cell phone is 3:52. How many minutes will pass before the phone next shows a time using each of the digits 2, 3, and 5 exactly once?

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problem

The time on a cell phone is 3:523:52. How many minutes will pass before the phone next shows a time using each of the digits 2, 3, and 5 exactly once?
Plain-text mathematical notation (without MathML)
The time on a cell phone is 3:52. How many minutes will pass before the phone next shows a time using each of the digits 2, 3, and 5 exactly once?
Original LaTeX notation
The time on a cell phone is $3:52$. How many minutes will pass before the phone next shows a time using each of the digits 2, 3, and 5 exactly once?

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