Question

Bob has invented a game with paper cups. He lines up 121 cups face down in a straight line from left to right and consecutively labels them from 1 to 121. Bob then walks from left to right down the line of cups, flipping all of the cups over. He returns to the left end of the line, then makes a second pass from left to right, this time flipping cups 2,4,6,8.... On the third pass, he flips cups 3,6,9,12.... He continues like this: On the ith pass, he flips over cups i,2i,3i,4i,.... (By “flip,” we mean changing the cup from face down to face up or vice versa.) After 121 passes, how many cups are face up?

Answer 1