4971.HardMath and Logic

Surprise test impossible logic?

  • A.The students are lazy
  • B.The professor lied
  • C.The test was on Monday
  • D.Paradox
Answer: Paradox

If the test hasn't happened by Thursday, the students know it must be Friday (so it's not a surprise). This logic continues backward to Monday, 'proving' it can never be a surprise.

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4972.HardMath and Logic

Sphere or Torus using rocks?

  • A.Throw a rock and see if it hits
  • B.Measure the shadow
  • C.Taste the surface
  • D.Perpendicular loops
Answer: Perpendicular loops

On a sphere, any two 'great circles' must intersect. On a torus, you can have a loop that goes around the center and another through the hole that never meet.

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4975.HardMath and Logic

Hourglass weigh more falling or at rest?

  • A.Less
  • B.Same
  • C.It varies randomly
  • D.More while falling
Answer: More while falling

When sand is in the air, its weight isn't recorded by the scale. However, the force of the sand hitting the bottom is greater than its static weight, resulting in a net increase during the flow.

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4986.MediumMath and Logic

Reverses left/right but not up/down?

  • A.It reverses up/down too
  • B.It's an optical illusion
  • C.Your eyes are curved
  • D.Inverts Z-axis
Answer: Inverts Z-axis

If you point your finger to the right, the mirror image points to the right. The reversal is actually in the 'depth' (front to back) dimension relative to the mirror's surface.

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4987.HardMath and Logic

Camel 3000 bananas, 1k km. Max reach?

  • A.1,000 bananas
  • B.0 bananas
  • C.1,500 bananas
  • D.533.3 bananas
Answer: 533.3 bananas

The camel must leave 'caches' of bananas. To minimize the 'cost' of travel, he moves the bananas in stages until the total supply matches his max capacity for the remaining distance.

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4988.MediumMath and Logic

Get fair toss from biased coin.

  • A.Toss it once
  • B.Toss it three times
  • C.You can't
  • D.Toss twice
Answer: Toss twice

If you toss twice, the probabilities of HT and TH are both (p * (1-p)). Since these are equal, assigning one to 'Heads' and the other to 'Tails' creates a fair 50/50 result.

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