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 Exponentiation Tables - originally courtesy of skeeter84 
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Posted on: Thu Mar 06, 2014 4:52 pm




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Post Exponentiation Tables - originally courtesy of skeeter84
2 digit table:

1 = 1^2, 1^3, 1^4, 1^5, 1^6, 1^7, 1^8
2 = 2^1
3 = 3^1
4 = 4^1
5 = 5^1
6 = 6^1
7 = 7^1
8 = 8^1, 2^3
9 = 3^2
16 = 2^4, 4^2
25 = 5^2
32 = 2^5
36 = 6^2
49 = 7^2
64 = 2^6, 4^3, 8^2
81 = 3^4
125 = 5^3
128 = 2^7
216 = 6^3
243 = 3^5
256 = 2^8
343 = 7^3
512 = 8^3
625 = 5^4
729 = 3^6
1,024 = 4^5
1,296 = 6^4
2,187 = 3^7
2,401 = 7^4
4,096 = 4^6, 8^4
6,561 = 3^8
7,776 = 6^5
15,625 = 5^6
16,384 = 4^7
16,807 = 7^5
32,768 = 8^5
65,536 = 4^8
78,125 = 5^7
117,649 = 7^6
262,144 = 8^6
279,936 = 6^7
390,625 = 5^8
1,679,616 = 6^8
2,097,152 = 8^7
5,764,801 = 7^8

So, are we having fun yet!? 


3 digit table:

1 = 1^(1^1), 1^(1^2), 1^(1^3), 1^(1^4), 1^(1^5), 1^(1^6), 1^(1^7), 1^(1^8), 1^(2^1), 1^(2^2), 1^(2^3), 1^(2^4), 
1^(2^5), 1^(2^6), 1^(2^7), 1^(2^8), 1^(3^1), 1^(3^2), 1^(3^3), 1^(3^4), 1^(3^5), 1^(3^6), 1^(3^7), 1^(3^8), 
1^(4^1), 1^(4^2), 1^(4^3), 1^(4^4), 1^(4^5), 1^(4^6), 1^(4^7), 1^(4^8), 1^(5^1), 1^(5^2), 1^(5^3), 1^(5^4),
1^(5^5), 1^(5^6), 1^(5^7), 1^(5^8), 1^(6^1), 1^(6^2), 1^(6^3), 1^(6^4), 1^(6^5), 1^(6^6), 1^(6^7), 1^(6^8), 
1^(7^1), 1^(7^2), 1^(7^3), 1^(7^4), 1^(7^5), 1^(7^6), 1^(7^7), 1^(7^8), 1^(8^1), 1^(8^2), 1^(8^3), 1^(8^4), 
1^(8^5), 1^(8^6), 1^(8^7), 1^(8^8)

2 = 2^(1^1), 2^(1^2), 2^(1^3), 2^(1^4), 2^(1^5), 2^(1^6), 2^(1^7), 2^(1^8)
3 = 3^(1^1), 3^(1^2), 3^(1^3), 3^(1^4), 3^(1^5), 3^(1^6), 3^(1^7), 3^(1^8)
4 = 4^(1^1), 4^(1^2), 4^(1^3), 4^(1^4), 4^(1^5), 4^(1^6), 4^(1^7), 4^(1^8), 2^(2^1) 
5 = 5^(1^1), 5^(1^2), 5^(1^3), 5^(1^4), 5^(1^5), 5^(1^6), 5^(1^7), 5^(1^8)
6 = 6^(1^1), 6^(1^2), 6^(1^3), 6^(1^4), 6^(1^5), 6^(1^6), 6^(1^7), 6^(1^8)
7 = 7^(1^1), 7^(1^2), 7^(1^3), 7^(1^4), 7^(1^5), 7^(1^6), 7^(1^7), 7^(1^8)
8 = 8^(1^1), 8^(1^2), 8^(1^3), 8^(1^4), 8^(1^5), 8^(1^6), 8^(1^7), 8^(1^8), 2^(3^1)
9 = 3^(2^1) 
16 = 2^(2^2), 2^(4^1), 4^(2^1) 
25 = 5^(2^1)
27 = 3^(3^1) 
32 = 2^(5^1)
36 = 6^(2^1)
49 = 7^(2^1)
64 = 2^(6^1), 4^(3^1), 8^(2^1)
81 = 3^(2^2), 3^(4^1)
125 = 5^(3^1)
128 = 2^(7^1)
216 = 6^(3^1)
243 = 3^(5^1)
256 = 2^(2^3), 2^(8^1), 4^(2^2), 4^(4^1)
343 = 7^(3^1)
512 = 2^(3^2), 8^(3^1) 
625 = 5^(2^2), 5^(4^1)
729 = 3^(6^1)
1,024 = 4^(5^1)
1,296 = 6^(2^2), 6^(4^1)
2,187 = 3^(7^1)
2,401 = 7^(2^2), 7^(4^1)
3,125 = 5^(5^1)
4,096 = 4^(6^1), 8^(2^2), 8^(4^1)
6,561 = 3^(2^3), 3^(8^1)
7,776 = 6^(5^1)
15,625 = 5^(6^1)
16,384 = 4^(7^1)
16,807 = 7^(5^1)
19,683 = 3^(3^2)
32,768 = 8^(5^1)
46,656 = 6^(6^1)
65,536 = 2^(2^4), 2^(4^2), 4^(2^3), 4^(8^1)
78,125 = 5^(7^1)
117,649 = 7^(6^1)
262,144 = 4^(3^2), 8^(6^1)
279,936 = 6^(7^1)
390,625 = 5^(2^3), 5^(8^1) 
823,543 = 7^(7^1)
1,679,616 = 6^(2^3), 6^(8^1)
1,953,125 = 5^(3^2)
2,097,152 = 8^(7^1)
5,764,801 = 7^(2^3), 7^(8^1)
10,077,696 = 6^(3^2)
16,777,216 = 8^(2^3), 8^(8^1)
33,554,432 = 2^(5^2)
40,353,607 = 7^(3^2)
43,046,721 = 3^(2^4), 3^(4^2) 
134,217,728 = 2^(3^3), 8^(3^2)
4,294,967,296 = 2^(2^5), 4^(2^4), 4^(4^2) 


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Posted on: Thu Mar 06, 2014 5:15 pm




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Post Re: Exponentiation Tables - originally courtesy of skeeter84
Thanks for re-posting (with permission [thumbup] )

I'm not sure why the original tables (at viewtopic.php?f=3&t=469) had to be deleted?

One of the puzzles with exponentiation has moved to the 'subscribers only' section, so the tables had to go?

Patrick


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Posted on: Fri Mar 07, 2014 3:00 am




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Joined: Tue Apr 24, 2012 7:47 pm
Post Re: Exponentiation Tables - originally courtesy of skeeter84
I had originally posted my exponentiation tables to help everybody else out. When the exponentiation puzzle became only for subscribers, I was upset that I no longer could access it. Having been blocked from a puzzle I helped other people to solve, I got "spiteful" and decided to trash my tables. And then skeeter84 had an idea - an AWFUL idea! *evil Grinch smile*


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Posted on: Fri Mar 07, 2014 9:57 am




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Joined: Thu May 12, 2011 11:58 pm
Post Re: Exponentiation Tables - originally courtesy of skeeter84
skeeter84 wrote:
I had originally posted my exponentiation tables to help everybody else out. When the exponentiation puzzle became only for subscribers, I was upset that I no longer could access it. Having been blocked from a puzzle I helped other people to solve, I got "spiteful" and decided to trash my tables. And then skeeter84 had an idea - an AWFUL idea! *evil Grinch smile*

Oh dear [scared]

There still is the 7x7 "multiop" on Mondays (but of course that hardly has exponentiation in it)
(I'm thinking the multiop should have 'bitwise OR' again)

My guess now is you'll start submitting user puzzles with exponentiation [lol]

Or I could replace one of the existing special puzzles (or a regular puzzle) with an exponentiation one?

Patrick


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Posted on: Fri Jan 30, 2015 2:16 pm




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Joined: Fri May 13, 2011 11:45 am
Post Re: Exponentiation Tables - originally courtesy of skeeter84
(edited by pnm, cropped the original image)

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Posted on: Mon Jun 27, 2016 4:35 pm




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Post Re: Exponentiation Tables - originally courtesy of skeeter84
frederick wrote:
So, are we having fun yet!? 


Yes, this table is AWESOME :-) I could stare at it for hours... by the way, you can get books with exponentation on calcudoku.org - 121 Advanced Puzzles is one of those books. It's fantastic for avid solvers who want to get more out of the website, and it's only 11 or 12 US dollars.


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Posted on: Tue Jun 28, 2016 5:02 am




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Joined: Tue Apr 24, 2012 7:47 pm
Post Re: Exponentiation Tables - originally courtesy of skeeter84
Thanks, marblevolcano - I'm glad you like my exponentiation tables. I also wanted to say thanks to veryevilking and pnm for the 2-digit table with the digits 1-12. I was thinking about making changes to my above tables to include 9's and maybe up to 12 at some point.


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Posted on: Tue Jun 28, 2016 9:55 am




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Joined: Thu May 12, 2011 11:58 pm
Post Re: Exponentiation Tables - originally courtesy of skeeter84
skeeter84 wrote:
Thanks, marblevolcano - I'm glad you like my exponentiation tables. I also wanted to say thanks to veryevilking and pnm for the 2-digit table with the digits 1-12.

Well I only cropped the image (it was 3000x4000 pixels or so, with the table taking up maybe 8% of the whole space).

That said, I'm now looking at the powers of 2 list, thinking something is not right (if you're in computing
you basically dream powers of 2 [tongue] ) - there are a few errors in there [sad]


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Posted on: Tue Jun 28, 2016 10:37 am




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Post Re: Exponentiation Tables - originally courtesy of skeeter84
pnm wrote:
I'm now looking at the powers of 2 list, thinking something is not right (if you're in computing
you basically dream powers of 2 [tongue] ) - there are a few errors in there [sad]


It's just from 2^17 upwards.


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Posted on: Wed Jun 29, 2016 7:58 pm




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Joined: Fri May 13, 2011 9:37 am
Post Re: Exponentiation Tables - originally courtesy of skeeter84
New table with good figures, when it shows up!


http://imgur.com/6gv7Lhb
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