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  1. b1soul added a post in a topic Weighing in a Harder Way   

    that was my initial answer too (3*2, measuring it twice after each time you divide by 3)

    but I realized that after dividing 27 into three 9-coin groups and measuring twice, you'll know whether the odd coin out is heavier or lighter, after that you'll only need to measure once after each time you divide by 3

    6 is the answer if the weighing device only tells you whether two groups of coins are the "same" or "different" in weight (no weighing device that I know of does only that)
    if the weighing device tells you which group of coins is heavier and which is lighter, the answer is 4
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  2. b1soul added a post in a topic Hole in a sphere   

    the answer is the volume of a sphere with a diameter of 6 (I can't remember the formula for spherical volume)

    my logic: if the remaining volume of the sphere is the same no matter the diameter of the cylinder, reduce the cylinder to a line with a length of 6 inches, the remaining volume is the sphere with a 6 inch diameter
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