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...

#Paradox #Diamond #Lexington #Hsu #Diamond7

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

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Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.
Stay on topic — we're all here to learn more about math and science, not to hear about your favorite get-rich-quick scheme or current world events.

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Math	Appears as
Remember to wrap math in `$` ... `$` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$

Comments

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?
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?
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?
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 - 6 years ago

Thank you for these!!!

Ashwin Padaki - 6 years ago

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

Ashwin Padaki - 6 years ago

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 - 6 years ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$