[math-fun] Self-column
Hello Math-Fun, We want to build a column of true statements; every step makes a true statement about the count of the letters involved so far in the column. Example of such a column: TWO T THREE E THREE H FOUR R ... Explanation: At stage 1 the column is made of this true statement about the column itself: "There are 2 T's so far in C" ("C" is short for "column") At stage 2 the column is made of this true statement about the column itself: "There are 3 E's so far in C" At stage 3 the column is made of this true statement about the column itself: "There are 3 H's so far in C" At stage 4 the column is made of this true statement about the column itself: "There are 4 R's so far in C" etc. There are lots of such "self-columns", but we want here the alphabetically first one. It will start, I guess, like this: ONE A ONE B FOUR O FIVE O FIVE E EIGHT E etc. Question: when will this column end? Best, É. à+ É. Catapulté de mon aPhone
Both B Couple C Double D Every V On Sun, Apr 10, 2016 at 10:25 AM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
Hello Math-Fun, We want to build a column of true statements; every step makes a true statement about the count of the letters involved so far in the column.
Example of such a column:
TWO T THREE E THREE H FOUR R ...
Explanation: At stage 1 the column is made of this true statement about the column itself: "There are 2 T's so far in C" ("C" is short for "column")
At stage 2 the column is made of this true statement about the column itself: "There are 3 E's so far in C"
At stage 3 the column is made of this true statement about the column itself: "There are 3 H's so far in C"
At stage 4 the column is made of this true statement about the column itself: "There are 4 R's so far in C"
etc.
There are lots of such "self-columns", but we want here the alphabetically first one.
It will start, I guess, like this:
ONE A ONE B FOUR O FIVE O FIVE E EIGHT E etc.
Question: when will this column end? Best, É.
à+ É. Catapulté de mon aPhone
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Anything wrong with: A B ?
On Apr 10, 2016, at 10:48 AM, Mike Stay <metaweta@gmail.com> wrote:
Both B Couple C Double D Every V
On Sun, Apr 10, 2016 at 10:25 AM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
Hello Math-Fun, We want to build a column of true statements; every step makes a true statement about the count of the letters involved so far in the column.
Example of such a column:
TWO T THREE E THREE H FOUR R ...
Explanation: At stage 1 the column is made of this true statement about the column itself: "There are 2 T's so far in C" ("C" is short for "column")
At stage 2 the column is made of this true statement about the column itself: "There are 3 E's so far in C"
At stage 3 the column is made of this true statement about the column itself: "There are 3 H's so far in C"
At stage 4 the column is made of this true statement about the column itself: "There are 4 R's so far in C"
etc.
There are lots of such "self-columns", but we want here the alphabetically first one.
It will start, I guess, like this:
ONE A ONE B FOUR O FIVE O FIVE E EIGHT E etc.
Question: when will this column end? Best, É.
à+ É. Catapulté de mon aPhone
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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Hello Jon, the "self-column" must -- at every step/storey -- have two elements: -- an English number followed by -- a capital letter This step/statement must be true: if I start the column with TWO W the statement is true -- but we must check if there is another true statement coming _before_ TWO W, this "before" being meant "in the alphabetical order". We see here that TWO O is true so far, for instance, and comes before TWO W. Checking all the true available statements, we find that the column _must_ start with ONE A (in French we would start with DEUX D, not UN A). Now, after ONE A we must find again the alphabetically true statement being the first to discribe a quantity of letters of the whole column, including the said statement. The only such count is ONE B. Now, before ONE C comes FOUR O, etc. Best, É.
Le 11 avr. 2016 à 03:49, Jon Ziegler <jonz@alumni.caltech.edu> a écrit :
Anything wrong with: A B ?
On Apr 10, 2016, at 10:48 AM, Mike Stay <metaweta@gmail.com> wrote:
Both B Couple C Double D Every V
On Sun, Apr 10, 2016 at 10:25 AM, Eric Angelini <Eric.Angelini@kntv.be> wrote:
Hello Math-Fun, We want to build a column of true statements; every step makes a true statement about the count of the letters involved so far in the column.
Example of such a column:
TWO T THREE E THREE H FOUR R ...
Explanation: At stage 1 the column is made of this true statement about the column itself: "There are 2 T's so far in C" ("C" is short for "column")
At stage 2 the column is made of this true statement about the column itself: "There are 3 E's so far in C"
At stage 3 the column is made of this true statement about the column itself: "There are 3 H's so far in C"
At stage 4 the column is made of this true statement about the column itself: "There are 4 R's so far in C"
etc.
There are lots of such "self-columns", but we want here the alphabetically first one.
It will start, I guess, like this:
ONE A ONE B FOUR O FIVE O FIVE E EIGHT E etc.
Question: when will this column end? Best, É.
à+ É. Catapulté de mon aPhone
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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Question: when will this column end?
Not any time soon. The usual caveats about English number words, especially no conjunctive "and". I actually managed to get a program to reproduce your initial terms (except for an additional 5 F between 5 E and 8 E). For the curious, here's a few more terms: http://chesswanks.com/num/AngeliniAlphabet.txt
Many thanks, Hans--well done, this is the equivalent in English of Neil's http://oeis.org/A102850. One could enter yr seq in the OEIS too, keeping the first number and concatenating it to 01 for A, 02 for B, 03 for C, ... 26 for Z. Best, É. Le 11 avr. 2016 à 07:22, Hans Havermann <gladhobo@teksavvy.com> a écrit :
Question: when will this column end?
Not any time soon. The usual caveats about English number words, especially no conjunctive "and". I actually managed to get a program to reproduce your initial terms (except for an additional 5 F between 5 E and 8 E). For the curious, here's a few more terms:
http://chesswanks.com/num/AngeliniAlphabet.txt _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
-
Eric Angelini -
Hans Havermann -
Jon Ziegler -
Mike Stay