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SOLUTIONS: Slide 1: 22 In 12 hours, the hour hand makes one full circle, while the minute hand makes 12 full circles. If an observer "sits" on the hour hand, he'll see that the hour hand does not move (with respect to him), while the minute hand makes 12 – 1 = 11 full circles (and the clock itself makes one circle in the backwards direction). While making each of these 11 circles, the minute hand makes right angle with the hour hand twice. So the answer is 2 × 11 = 22. Slide 2: area = 24 square inches