# Math riddle - the power of exponent

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hi i have here a nice question that i personaly very fond of: how much ink would it take to write down 4^(4^(4^4))) if you would write the result digit by digit ? ill make it multiple choice: 0) 1000 pens worth of ink 1) a bucket full of ink 2) the great lakes full of ink 3) the all the oceans full of ink 4) the entire planet volume filled with ink 5) the volume of the sun worth of ink 6) a ball as large as the solar system worth of ink 7) a ball as large as the galexy 8) the entire universe's volume (as the big bang theory) filled with ink i will post the solution 1 day from now. Iftah.

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Well, you don't specify how many digits you can write per volume of ink. Maybe this number can be estimated, but it could also be open to interpretation. (we don't know if there needs to be enough ink so that the digit is legible to the human eye, or if an atom-wide streak of ink would suffice).

Say for example, I do some crazy math and say the answer is 4. Someone else could come along with a different interpretation of the ink-to-digit ratio and probably argue that the answer is actually 3 or 5.

So if we assume that the riddle is well-founded (that it has one definitely correct answer that is not open to reinterpretation), then the only answer that could possibly survive as not being open to reinterpretation would be to say the biggest possible one, 8.

No math needed =D

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I think it's big enough such that it doens't matter how you interprit ink. the answer is 7 or 8 I guess 8

4^exp, the exp was on the order of 10^125 so I'm assuming 4^ that would be biger then the galexy.

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Yeah, in terms of actually doing the numbers and not cheating..

I did a search and found that the number of atoms in the universe is estimated at 10^79 or 10^80. So 4^256 = 16^128 is definitely bigger than that. Four to the power of that number would be a might bigger.

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The universe contains on the order of 1080 neutrons, so there wouldn't be enough matter in the universe to do it even if each digit only took one atom. However, the Big Bang theory in its classical form posits that the VOLUME of the universe is infinite, so (8) isn't correct either. So, none of the above.

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Hmmm, the right answer isn't there. I just wrote down 4^(4^(4^(4^4)))) and it didn't even take one pen's full of ink.

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Quote:
 Original post by Anonymous PosterHmmm, the right answer isn't there. I just wrote down 4^(4^(4^(4^4)))) and it didn't even take one pen's full of ink.

Hm. Try pushing harder with the pen.

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Quote:
 Original post by SneftelThe universe contains on the order of 1080 neutrons, so there wouldn't be enough matter in the universe to do it even if each digit only took one atom. However, the Big Bang theory in its classical form posits that the VOLUME of the universe is infinite, so (8) isn't correct either. So, none of the above.

Great! This one. No doubt.

4^(4^(4^4))) = 4^(4^256)) ~ 410154

And of course this is a number out of imagination.

I've read that also the number of all the possible combinations of moves in a chess game is a number >> number of electrons

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check out this: http://en.wikipedia.org/wiki/Arrow_notation ;)

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Quote:
 Original post by Iftahhow much ink would it take to write down 4^(4^(4^4))) if you would write the result digit by digit ?

None. I always write in pencil [wink].

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