Wednesday, 6 April 2011

The infinite arrow

Aaand pezasied nabs it: This puzzle is meant to be said out loud, as it's a play on words. "A toad" is supposed to sound like "eight owed," so the wizard walks out of the store with £1 and eight owed. £8 plus the £1 he already payed, the total amount for the toad was £9


There's just no fooling you guys is there?! The next puzzle is grounded in a mathematical concept that not everyone may be aware of. You'd need to be a veritable Robin Hood to see through this one. I'll see how you guys do:

Imagine an arrow in flight, travelling toward its target. Before it reaches the bullseye, it must first travel half of the distance from the archer to the board. Then, it must travel half of the remaining distance. Then, half of that remaining distance, ad infinitum. For example, if there is 10m between the archer and the tree, it must first travel 5m, then the next 2.5m, then the next 1.25m, and so forth. In this way, you can see that the distances become smaller and smaller. 


The question is, will the arrow ever meet its mark?

37 comments:

  1. Another interesting read! Great blogger!

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  2. Good article, makes you think :)

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  3. ha, the number gets so small that it is good enough to be called touching. besides. Due to the fact that atoms exert a force on other atoms nothing ever really touches anything. we only experience the forces of the atoms pushing on one another.

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  4. looks like vashrave reads on quantum theory, good for him.

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  5. I refuse to believe they sound alike, but maybe it's just my accent. Oh well.

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  6. If that is so, the arrow will never meet its mark. It'll always come 50% closer to it. That means that even if it's 0.2 mm away, it'll travel to 0.1 mm. It'll come terribly close to hitting the mark, but never will truly touch it.

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  7. I didn't understand the puzzle?

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  8. I don't know, this is too mathematical for me.

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  9. hmm.. agree with Fang here. the arrow will never truly touch the board.

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  10. A picture would be appreciated, didn't get the problem :(

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  11. I would say no as even if it is halved to infinity, it would eventually be traveling a distance of Planck length(1.163*10^-35).
    IE: Much smaller than a neutrino which is so tiny that it can pass through matter almost undisturbed. Strings(1D) in String theory exist at this level.
    Any length shorter than Planck length makes no sense given the laws of physics and quantum mechanics that are agreed upon by the scientific community today. That's just a quick guess though. However, it would seem like the general consesus here is no. But then again if we're looking at it on a atomic level, what vashrave said would be true. I'm curious to know the answer.

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  12. not much of a puzzle, right?
    but it sure will, because the curve will, sometime reach D = 0, that is, it will reach the target.

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  13. quantum theory in this one tbbt

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  14. I knew the last one, but I have no idea here

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  15. No, not if it keeps halving the distance between it and the target. Yeah, I say that so fast like I'm a genius.

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  16. not if my cock blocks the arrow

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  17. this is called the something, something principle....

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  18. I believe the arrow will use limits and stuff to solve.

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  19. i know computers think .99999999999999~ is 1? is this the same concept?

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  20. You just divided by zero didn't you?

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  21. Yep. Zeno's paradox (sort of).

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  22. But even if it has to travel the half of the half it will eventually travel the half of the half at some point.

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  23. Nope it wont.
    Good rule If you have a roommate;
    Take no more than half the sugar.. that way there will ALWAYS be some left^^

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  24. I thought its a simple limit of a geometric series. Mathematically, the formula for the series of each halving of the distance will be 5/(2^n) from n=0 to n=infinity. As |r| < 1 the series diverges and the entire distance traveled is the sum of this series. The formula for the entire distance traveled is a/(1-r) where a=5 and r=0.5 (from 5/(2^n)) So the total distance traveled is 5/(1-0.5)=10. Sorry if this is hard to follow, it made more sense in my brain.

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