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Mathematical Paradoxes

I don't know why I started this discussion... but...

If you have any mathematical paradoxes you know, feel free to post them here. This could get interesting...

Note by Ashwin Padaki
2 years, 6 months ago

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  Easy Math Editor

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2^{34} \( 2^{34} \)
a_{i-1} \( a_{i-1} \)
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\sum_{i=1}^3 \( \sum_{i=1}^3 \)
\sin \theta \( \sin \theta \)
\boxed{123} \( \boxed{123} \)

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  1. A jackpot is currently worth \(1\) dollar. Every time I toss a head on a fair coin, the jackpot doubles, but when I toss a tail, the game ends and I take home the jackpot. How much should I be willing to pay to play this game?

  2. I have two envelopes, and am told that one of them has twice as much cash as the other. I open Envelope 1 up. Should I stick to it or switch? Wait, but the envelopes are the same. Why is it that I should always switch to Envelope 2?

  3. In a casino game, a random number \(x\) in the interval \((0, 1)\) is generated on a calculator, and I win \(\frac{1}{x}\) dollars. How much should I be willing to pay to play this game?

  4. Player A and Player B are in a 100 meter race. Player A is at the 50 meter mark, walking at \(1\) \(m/s\). Player B is at the 20 meter mark, sprinting at \(10\) \(m/s\). When Player B reaches the 50 meter mark, player A would've covered some distance by then. Then, when Player B reaches that point, Player A would've walked some more, and so on. Therefore, Player B will never catch up with Player A, and lose the race.

Alex Li - 2 years, 6 months ago

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I am also interested in #2. I would think the probability would be 50 50.

Ashwin Padaki - 2 years, 6 months ago

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Thank you for these!!!

Ashwin Padaki - 2 years, 6 months ago

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I think I have an answer to the 4th one A would be moving but will cover less distance than B in the same time interval......... Therefore at some time B will cross A.

Jahnvi Verma - 2 years, 6 months ago

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