You enter a magical cave to find seven orbs. A wizard tells you that each orb is colored on the inside, and that four or more of the orbs have the same color. Also, when two orbs of the same color are brought into contact with each other, they will glow, revealing the color. If two orbs touch but have different color, nothing happens. The orbs are heavy, so you can only touch two at a time. What is the least number of comparisons needed to find one of the orbs of the majority color?
Problem Solving by Thomas DeFranco and Charles Vinsonhaler.