In a supervillain's top-secret lab there is a row of 60 buttons that glow red when pressed once, and turn off when pressed again. Every night the strict head scientist makes sure all the lights are turned off. One day, a group of 60 super-smart chimps from the lab decide to play a prank.
The chimps line up an hour before the scientist arrives. The first chimp walks along the row and presses every button once, turning on all the lights. The next chimp follows by pressing every other button once startingatthesecondbuttonstartingatthesecondbutton. Chimp 3 then goes to every third button startingwiththethirdstartingwiththethird and turns it on if off, and off if on. Chimp 4 follows by pressing every fourth button if it’s off and switching it on if it’s off. This goes on and on until chimp 60 finally goes to the sixtieth button. When the head scientist arrives later in the morning, how many lights does she find turned on?
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7
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