bonanova
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Everything posted by bonanova
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No one has it yet ... Try slicing it up to be able to look inside.
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superprism has it. Nice.
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A bit longer.
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You're probably thinking of L'Hopital's rule where limits of functions are in view. The OP does not refer to functions or limits, just two references to "infinity." Since infinity comes in different flavors [cardinalities] it's no so simple as saying infinity2/infinity = infinity. If the infinity in the denominator is C and in the numerator is [Aleph0]2, then the result is zero.
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Two circular cylinders of unit radius intersect at right angles so that their axes intersect as well. What is the volume common to both cylinders? What if there were three cylinders?
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Nice try but check B5-G7 with D2-F7, and B5-G2 with D2-G7.
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Right - 0 and 2. Choke up on the bat a bit ... ... or just look at the puzzle from a different angle.
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Check that you end up with a square that way ...
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You can do better. That's like saying the largest line segment in a square is the side of a square.
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This solution might take 2nd place. Whose theory limits it to that number?
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No one has it yet. All answers so far are on the high side. The problem simplifies with a particular point of view.
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What's the area of the smallest ellipse that contains the 3-4-5 triangle? What's the area of the largest ellipse that fits inside the 3-4-5 triangle? This will test your calculus or your logic. Enjoy.
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plainglazed has it. Can you do it without talking to Pythagoras? See spoiler in OP
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DeeGee has it. Kudos.
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An old favorite asks us to express the integers using only four 4's. For example: 1 = 44/44; 2 = 4/4 + 4/4. Irrationally perhaps, it has been suggested that we use pi instead. We are allowed the operations of addition, subtraction, multiplication, division, square root and floor. Floor, indicated by brackets, is simply the largest whole number: 3 = [pi]. Can you express the numbers 1-20 using 4 or fewer pi's? Using spoilers, of course. Enjoy.
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What is the largest number that can expressed in conventional notation using no symbols other than three digits?
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What is the largest number of pawns on a 7x7 chess board whose pairwise distances are all different? Assume that the pawns lie in the center of their individual squares, and distances are measured on a straight line joining their centers.
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For question 5 is it assumed that you are the first player?
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A circular [annular] race track has a constant width of w meters. If the longest straight-line distance entirely on the track is 12 meters, what is the area of the track? [Excluding the circular infield.]
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It's trivial to ask the size of the largest point that will will fit on a unit line segment. And it's not much harder to determine the largest line segment that will fit in a unit square. So let's ask instead: What is the largest square that will fit in a unit cube? The largest hexagon?
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Obviously, the reason why a three legged chair is better, is that it is easier to position it such that the stool is flat. Though all four legs are on the floor, the table is very unlikely in a horizontal position. In addition, the legs are certainly not necessarily square to the part of floor on which they stand. Yes. That does it.
