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Mirelo
 Expert Boarder
Posts: 87 
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40 39 38 37 36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3
Simple. 10 is congruent to 1 mod 3. Therefore 10 to the power N is congruent to 1 to the power N, which is 1, for any positive integer N.
Therefore a googol = 10^100 is congruent to 1 mod 3. A googolplex has googol+1 digits, so the number of digits is congruent to 2 mod 3. So there are 2 digits before the first comma.
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kdavis004
Senior Boarder
Posts: 77
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Mark Brader schrieb:
Another way to put it is that if you compute 10^N - 1, you get a number with all digits 9, and that is divisible by 3; so all numbers of the form 10^N have a remainder of 1 when divided by 3.
A googolplex = 10,000,.....
Mark, you have beaten me to the solution yet again!  Cheers |
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Sweety
Senior Boarder
Posts: 73
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Well, somebody had to do it! |
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iphwin
Expert Boarder
Posts: 83
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Yeah Exactly. Moreover the answer is always the same for all the below
10^10 10^100 10^1000 10^10000 10^100000 and so on....
In effect for 10^10^N where N is any whole number there are always 2 digits 1 and 0 before the comma.
Thanks Kannappan
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swasta
Expert Boarder
Posts: 81
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It's fairly well-known that the modulus 3 of N equals the modulus 3 of the sum of the digits of N. The digits of a google one are 1 + lots of 0's + 1, which sum to 2.
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dagger29
 Expert Boarder
Posts: 85
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Ed Murphy schrieb:
Just when you thought the solution couldn't become any simpler, it suddenly does.
Cheers |
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dagny
Senior Boarder
Posts: 69
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Heh - Carl Sagan once started unrolling a paper tape (like a cash register tape) with the beginning of a googleplex on it in marking pen, and he started walking down the street unrolling this tape, and across town, and all over the place - through the park, etc, for dramatic effect of course - he runs out of tape, and says, 'A piece of paper big enough to write the number 'one googleplex' could not be _stuffed_ into the _known Universe_!' emphasis his, of course. 
Cheers! |
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bhunders
Senior Boarder
Posts: 78
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Ah the miracle of the internet. Impossible on paper, yet here you've done it three times in one post.
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Chamrin
Senior Boarder
Posts: 78
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Not even in billions and billions of years?
Bill Smythe
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quest_marsman
Expert Boarder
Posts: 83
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Bill Smythe schrieb:
Not even in billions to the power of billions years, I think.
Cheers
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MishaEE
Senior Boarder
Posts: 68
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Just in case you're serious, 'Billions and billions' is one of the most famous things he never said, except once, in an interview, just kind of like, 'Aw, ok, billions and billions, ha ha' when the interviewer asked him about it. He did say, however, that he did emphasize the 'B' sound, so that people wouldn't think he was talking about mere millions.
Cheers! |
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