Question 117
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?