Puzzle 76
I took a logic class in college that met five days a week, Monday through Friday, and one Monday, at the very beginning of class, the teacher announced, “In one class meeting this week, I will give you a surprise quiz.” Since this was a logic class, we were all able to figure out which was the only day he could give us the quiz. Which day was it? (It’s not enough to show why your answer works; you must also show why each of the other four possible days does not work.)
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Puzzle 77
The numbers, 3, 4, 5, 6 and 7, are typed and printed onto five distinct cards, arranged in an addition column, and the same is true for the numbers, 8, 7, 6, 3 and 2. Exchange one card from the first column with one card from the second column in such a way as to get the same sum in both columns.
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Puzzle 78
This one is for high school geometry students. Without using Heron’s Formula, which is usually not taught in a basic geometry course, anyway, find the area of a triangle whose sides measure 13, 14 and 15.
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Puzzle 79
You are in a race and you overtake the person who is in first place. What place are you in, now? OK, so you got that one right away. How about this one: You are in a race and you overtake the person who is in last place. What place are you in, now?
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Puzzle 80
Find unequal rational numbers, a and b (other than 2 and 4), such that .