3.1. Along the groove, there are 100 multi-colored balls arranged in a row with a periodic repetition of colors in the following order: red, yellow, green, blue, purple. What color is the ball at the $78-$th position?

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3.1. Since 5 colors repeat periodically, all balls whose position numbers give the same remainder when divided by 5 will have the same color. When 78 is divided by 5, the remainder is 3. Therefore, the color of the ball in the 78th position will be the same as that of the ball in the third position, i.e., green.