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Omni-MATH / A malfunctioning digital clock shows the time 9:57AM; however, the correct time is 10:10AM. There are two buttons on the clock, one of which increases the time displayed by 9 minut…

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problem

A malfunctioning digital clock shows the time 9:57AM9: 57 \mathrm{AM}; however, the correct time is 10:10AM10: 10 \mathrm{AM}. There are two buttons on the clock, one of which increases the time displayed by 9 minutes, and another which decreases the time by 20 minutes. What is the minimum number of button presses necessary to correctly set the clock to the correct time?
Plain-text mathematical notation (without MathML)
A malfunctioning digital clock shows the time 9:57AM; however, the correct time is 10:10AM. There are two buttons on the clock, one of which increases the time displayed by 9 minutes, and another which decreases the time by 20 minutes. What is the minimum number of button presses necessary to correctly set the clock to the correct time?
Original LaTeX notation
A malfunctioning digital clock shows the time $9: 57 \mathrm{AM}$; however, the correct time is $10: 10 \mathrm{AM}$. There are two buttons on the clock, one of which increases the time displayed by 9 minutes, and another which decreases the time by 20 minutes. What is the minimum number of button presses necessary to correctly set the clock to the correct time?

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