Infinitely many mathematicians are locked in a dungeon by an evil wizard. The evil wizard makes them stand in a line, with one person in the back, a person in front of him, a person in front of them, etc, each person facing towards the front.
The wizard puts a hat on the head of each person, which can be of one of infinitely many colors. Each person can see all the hat colors of the people in front of them, but not their hat, nor the hats of the people behind them. Then, starting from the back, he asks each person in turn what color their hat is. If they are correct, they live, otherwise they die. In either event, everyone can hear each answer, and whether the speaker lives or dies.
The mathematicians are given time to figure out how they should guess before they are lined up.
What is the best possible system? In other words, what method of guessing guarentees as many mathematicians live as possible?
martinrebas: happens? The infinite rod descends freely through the first 90 degrees, until it’s parallel to the tabletop. But it can’t go beyond this, because then at some point the solid rod would intersect the solid table.
Thus it’s impossible to “rest” an infinite rod on an infinite plane. “And so, you have the curious phenomenon of the hinged rod being
Phyllis Harmonic: With no beginning and no end, the only "location" on an infinitely long line would be the exact middle, right? Same for infinite volume- we would be forever at the exact center. All of us at once (assuming we are occupying the same infinite volume.)
andreaazure: The thing that always got me is that i is not so much "undefined" as "simultaneously both the largest and smallest possible number." When I pointed this out in my third (?) grade Catholic school math class, the teacher/nun was not happy.
1 / -5 = -.2
1 / -2 = -.5
1 / -1 = -1
1 / -.5 = -5
1 / -.1 = -10
1 / 0 = Inf1, where Inf1is the smallest of all numbers, negative infinity. -∞
1 / 0 = Inf2, where Inf2 is the largest of all numbers, infinity. ∞
1 / .1 = 10
1 / .5 = 2
1 / 1 = 1
1 / 2 = .5
1 / 3 = .33
1 / 10 = .1
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