This World and Me

Here's a mind-blowing logic puzzle that my math professor shared last week. Problem A long time ago, there lived a tribe of 100 green-eyed dragons. These dragons had a rule: if any dragon in the tribe deduces what the color of his eyes was, then that dragon must commit ritual suicide by the end of that day. Aside from this, the dragons lived peacefully. Although each dragon could see the eye color of every other dragon, no dragon was cruel enough to discuss eye colors with other dragons. For all each dragon knew, he or she could be the one dragon that had blue eyes among 99 green-eyed dragons. One day, however, a visitor arrives to the tribe. On the day she arrives – we will call this day 1 – she remarks, "I see a dragon with green eyes." The visitor leaves later that day. At the end of day 1, no dragon in the tribe performs the ritual. At the end of the next day (day 2), no one performs the ritual. In fact, after the visitor leaves, the dragons continue to live in p...

Consider the following. Before you stands a heap of sand. You have just returned home from the beach, and while there, you grabbed a bunch of sand, placed it in a jar, took it home, and dumped it onto the floor. These individual grains of sand are collectively a heap . We can both agree to this as “heap” is a rather vague description for a mound or pile of a particular substance. Now, there are probably hundreds upon hundreds of grains of sand in this heap. Let’s suppose there are exactly 10,000 grains. If we take exactly one grain of sand out of the heap, we would then have 9,999 grains of sand, and we would both still agree that 9,999 grains of sand is a heap. Likewise, if we remove another grain of sand, we are left with 9,998 grains, and it would still be a heap. Removing one grain of sand is so trivial a difference that it does not change whether the remaining grains are a heap. You might already see a potential problem with this argument. If we accept the premise that removing o...

Consider this scenario. The instructor of one of your classes promises you that there will be a surprise quiz next week. The class in question meets only on Mondays, Wednesdays, and Fridays, and a "surprise" quiz is one which, walking into the classroom, you have no idea whether it will be given on that day. The school week ends on Friday, so there are only three possible dates for the quiz: next Monday, next Wednesday, and next Friday. If you came to class on both Monday and Wednesday, and on both days, there were no quizzes, then you would know, walking into class on Friday, that there must be a quiz, for Friday is the last remaining day in which the instructor could give a quiz as promised that week.  Therefore, it would not be a surprise for the instructor to give a quiz on Friday. Because Friday has now been eliminated, Monday and Wednesday are the only possibilities left for the surprise quiz. If you came to class on Monday and were not given a quiz, then Wednesday...

We often wonder what it is about humans that sets us apart from every other species of life on Earth. We can communicate with each other in languages more complex than any other life form; we can invent tools and machines that make life for us longer and easier. We have the stunning ability to prove the truth with our minds—and we do this through reason. The 18th-century Age of Enlightenment sealed the deal for reason, establishing it as the highest source of authority for mankind. If there is any one trait that sets us apart from all other life on Earth, it has to be our impeccable ability to reason: the ability to conclude that if all humans are mortal, and Mr. Stroh is a human, then Mr. Stroh must be mortal. The foundations for reasoning are the rules of logic—and so too are the foundations for mathematics. Fermat’s Last Theorem states that equation x n + y n = z n will have no whole number solutions when n > 2. The theorem was proposed by French mathematician Pierre de ...