Selfreferential ``this sentence has'' sentences in base two, exhaustive list  there are no others.
1. This sentence has one thousand one hundred a's, one b, ten c's, eleven thousand one hundred eleven d's, one million e's, one f, one g, ten thousand one hundred ten h's, one hundred ten i's, one j, one k, one thousand ten l's, eleven m's, one million one n's, one hundred thousand one hundred ten o's, one p, one q, one thousand eleven r's, eleven thousand one hundred s's, ten thousand one hundred one t's, ten thousand one hundred u's, one hundred ten v's, one w, and one x.
2. This sentence has one thousand one hundred a's, one b, ten c's, eleven thousand one hundred one d's, one million one e's, one f, one g, ten thousand one hundred one h's, one hundred ten i's, one j, one k, one thousand ten l's, eleven m's, one million ten n's, one hundred thousand one hundred eleven o's, one p, one q, one thousand ten r's, eleven thousand one hundred s's, ten thousand one hundred ten t's, ten thousand eleven u's, one hundred ten v's, one w, one x, and one y.
3. This sentence has one thousand one hundred a's, one b, ten c's, one hundred thousand one d's, one million one hundred e's, one f, one g, ten thousand one hundred eleven h's, one hundred ten i's, one j, one k, one thousand ten l's, eleven m's, one million one hundred one n's, one hundred one thousand eleven o's, one p, one q, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand eleven t's, ten thousand one hundred one u's, one hundred ten v's, one w, one x, one y, and one z.
4. This sentence has one thousand one hundred a's, one b, ten c's, one hundred thousand one d's, one million one hundred one e's, one f, one g, ten thousand one hundred eleven h's, one hundred ten i's, one j, one k, one thousand eleven l's, eleven m's, one million one hundred n's, one hundred one thousand eleven o's, one p, one q, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand one t's, ten thousand one hundred one u's, one hundred eleven v's, one w, one x, and one y.
5. This sentence has one thousand one hundred a's, one b, ten c's, one hundred thousand one d's, one million one hundred ten e's, one f, one g, ten thousand one hundred eleven h's, one hundred ten i's, one j, one k, one thousand eleven l's, eleven m's, one million one hundred one n's, one hundred one thousand ten o's, one p, one q, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand eleven t's, ten thousand one hundred one u's, one hundred eleven v's, one w, one x, and one y.
6. This sentence has one thousand one hundred eleven a's, ten c's, eleven thousand one hundred ten d's, one hundred eleven thousand one hundred ten e's, ten thousand one hundred eleven h's, ten i's, one thousand ten l's, one hundred eleven thousand n's, eleven thousand eleven o's, one thousand one r's, eleven thousand one hundred ten s's, eleven thousand t's, ten thousand one hundred one u's, and one thousand ten v's.
7. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand d's, one hundred eleven thousand one e's, eleven thousand h's, ten i's, one thousand l's, one hundred ten thousand one hundred eleven n's, eleven thousand one hundred o's, one thousand ten r's, eleven thousand one hundred ten s's, ten thousand one hundred eleven t's, ten thousand one hundred ten u's, and one thousand v's.
8. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand one hundred d's, one hundred eleven thousand one hundred eleven e's, one f, one g, eleven thousand ten h's, ten i's, one j, one thousand l's, one hundred eleven thousand one hundred one n's, one hundred thousand ten o's, one thousand one hundred r's, eleven thousand one hundred ten s's, ten thousand one hundred one t's, eleven thousand u's, and one thousand v's.
9. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand one hundred ten d's, one million ten thousand one hundred e's, one f, one g, eleven thousand eleven h's, one hundred ten i's, one j, one k, one thousand one hundred eleven l's, eleven m's, one million one thousand one hundred ten n's, one hundred one thousand one hundred eleven o's, one p, one q, one thousand one hundred one r's, eleven thousand one hundred eleven s's, ten thousand one hundred one t's, eleven thousand one u's, one thousand eleven v's, one w, and one x.
10. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand ten d's, one million one thousand one hundred e's, one f, one g, eleven thousand one h's, one hundred ten i's, one j, one k, one thousand one hundred one l's, eleven m's, one million one thousand ten n's, one hundred one thousand one hundred eleven o's, one p, one q, one thousand eleven r's, eleven thousand one hundred eleven s's, ten thousand one hundred one t's, ten thousand one hundred eleven u's, one thousand one v's, one w, and one x.
11. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand ten d's, one million one thousand one hundred eleven e's, one f, one g, eleven thousand one h's, one hundred ten i's, one j, one k, one thousand one hundred eleven l's, eleven m's, one million one thousand one n's, one hundred one thousand one hundred one o's, one p, one q, one thousand eleven r's, eleven thousand one hundred eleven s's, ten thousand one hundred t's, ten thousand one hundred eleven u's, one thousand eleven v's, and one w.
12. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand ten d's, one million one thousand one hundred eleven e's, one f, one g, eleven thousand one h's, one hundred ten i's, one j, one k, one thousand one hundred one l's, eleven m's, one million one thousand one hundred one n's, one hundred ten thousand one o's, one p, one q, one thousand eleven r's, eleven thousand one hundred eleven s's, ten thousand one hundred ten t's, ten thousand one hundred eleven u's, one thousand one v's, one w, one x, one y, and one z.
13. This sentence has one thousand one hundred eleven a's, one b, ten c's, one hundred thousand ten d's, one million ten thousand one e's, one f, one g, eleven thousand one h's, one hundred ten i's, one j, one k, one thousand one hundred ten l's, eleven m's, one million one thousand one hundred one n's, one hundred one thousand one hundred eleven o's, one p, one q, one thousand eleven r's, eleven thousand one hundred eleven s's, ten thousand one hundred eleven t's, ten thousand one hundred eleven u's, one thousand ten v's, one w, one x, one y, and one z.
14. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand one hundred d's, one million e's, one f, one g, eleven thousand one h's, one hundred i's, one thousand one l's, ten m's, one hundred eleven thousand one hundred eleven n's, one hundred thousand one hundred one o's, one thousand one hundred one r's, eleven thousand one hundred one s's, ten thousand ten t's, ten thousand one hundred eleven u's, and one hundred eleven v's.
15. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand one hundred d's, one million one hundred eleven e's, one f, one g, eleven thousand one h's, one hundred ten i's, one j, one k, one thousand ten l's, eleven m's, one million one thousand one n's, one hundred one thousand one hundred ten o's, one p, one q, one thousand one hundred one r's, eleven thousand one hundred one s's, ten thousand one hundred t's, ten thousand one hundred eleven u's, one hundred ten v's, one w, and one x.
16. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand one hundred ten d's, one hundred eleven thousand one hundred one e's, one f, eleven thousand ten h's, ten i's, one hundred ten l's, one hundred eleven thousand one hundred one n's, one hundred thousand o's, one thousand one hundred ten r's, eleven thousand one hundred s's, ten thousand one hundred one t's, eleven thousand u's, and one hundred ten v's.
17. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand ten d's, one hundred eleven thousand e's, one f, eleven thousand h's, ten i's, one hundred ten l's, one hundred eleven thousand n's, eleven thousand one hundred one o's, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand one hundred one t's, ten thousand one hundred ten u's, and one hundred ten v's.
18. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand ten d's, one hundred eleven thousand e's, one f, one g, eleven thousand h's, ten i's, one hundred ten l's, one hundred eleven thousand n's, eleven thousand one hundred o's, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand one hundred ten t's, ten thousand one hundred ten u's, and one hundred ten v's.
19. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand ten d's, one hundred eleven thousand e's, one f, one g, eleven thousand h's, ten i's, one j, one k, one hundred one l's, one hundred eleven thousand ten n's, one hundred thousand one o's, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand one hundred t's, ten thousand one hundred ten u's, and one hundred one v's.
20. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand ten d's, one hundred eleven thousand one e's, eleven thousand h's, ten i's, one hundred ten l's, one hundred eleven thousand one n's, eleven thousand one hundred one o's, one thousand one hundred r's, eleven thousand one hundred s's, ten thousand one hundred ten t's, ten thousand one hundred ten u's, and one hundred ten v's.
21. This sentence has one thousand one hundred one a's, one b, ten c's, one hundred thousand ten d's, one million e's, one f, one g, eleven thousand h's, one hundred i's, one j, one k, one thousand one l's, ten m's, one hundred eleven thousand one hundred eleven n's, one hundred thousand one hundred one o's, one p, one thousand one hundred r's, eleven thousand one hundred one s's, ten thousand eleven t's, ten thousand one hundred ten u's, and one hundred eleven v's.
Selfreference 1999 computations preserved from deletion by att worldnet's demise. Note: singletons are moved as far forward in the alphabet as possible below. Thus sentences with a z are also pangrams. Computations were done with binary decision diagrams (BDD's). Public domain, distribute freely with or without attribution.
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 SelfReferential Sentences: Base Ten
 SelfReferential Sentences: Base Ten
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Cute, but incorrect. "Ten" does not refer to the pattern of symbols 10, but to one more than "nine" regardless of the radix. The first sentence has 1100 instances of the letter A if you represent the count in base 2, but this is still "twelve" (being one more than "eleven" and one less than "thirteen") not "one thousand, one hundred."
ReplyDeleteOn the contrary, you hear "What's one hundred octal?" all the time. The name refers to the name of the symbol sequence, not the underlying number.
DeleteThank you. Binary is not read like decimal.
ReplyDelete