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In a long room are three doors. Behind each door one block is hanging from the ceiling. Behind the first door the block is made of concrete; behind the second door the block is made of hardwood; behind the third door the block is made of styrofoam. The rectangular base of each block is 5 cm by 6 cm = 30 square cm. The height of each block is unknown. The distance from the ceiling to the base of each block is unknown but the base of each block is more that 1.8 meters above the floor. The distance from the floor to the ceiling is 3 meters. When an 1.8 meter tall man enters the room the block immediately drops onto his head.

The question is, which of the three doors he should choose to enter so the damage to himself is minimal?


The trick to this question is that the result remains the same whether the thickness of the block is minimum or maximum. The maximum thickness is 60 cm. The minimum thickness, practically speaking, is 0.5 cm. When the thickness is maximum, the speed upon impact is 3.42 m/s. When the thickness is minimum, the speed upon impact is 4.83 m/s. So in both cases, the force upon impact is minimum for the styrofoam block. I consider this question is a minimum/maximum problem, because anything in between is inconclusive.

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    $\begingroup$ I’m voting to close this question because it's not a puzzle - there doesn't appear to be any trick, just common sense $\endgroup$
    – bobble
    Jul 31 at 0:59
  • $\begingroup$ If the concrete block has 0.5 cm thickness, then the block weighs 37.5 g. If the styrofoam has the 60 cm thickness, , then it weighs 90 g. In addition, we have to consider the speed with which the two blocks fall. $\endgroup$ Jul 31 at 2:16
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    $\begingroup$ Sure, but both of those are unknowns. We don't have a way to calculate the weight of the blocks, nor the force of impact. In the absence of that it does seem like the answer is just door 3 because the styrofoam is least likely to hurt. $\endgroup$ Jul 31 at 2:48
  • $\begingroup$ The three blocks fall at the same speed, unless we calculate air resistance. And even then, the only block that will fall slower is the styrofoam one. $\endgroup$
    – Exal
    Jul 31 at 2:51
  • $\begingroup$ @ Exal. The speed of the falling blocks depends on the distance they travel. $\endgroup$ Jul 31 at 4:10
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Solution:

The man should enter the third door.

Reasoning:

Styrofoam doesn't hurt as much as hardwood or concrete.

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  • $\begingroup$ One cubis centimeter of concrete weighs 2.5 g. One cubic centimeter of styrofoam weighs 0.05 g. I hope this will help you to make the calculations while thinking more creatively. $\endgroup$ Jul 31 at 1:34

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