Self-reference 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.

Monday, January 4, 2010

Self-Referential Sentences: Base Three

Self-referential ``this sentence has'' sentences in base three, exhaustive list - there are no others.


1. This sentence has twelve a's, one b, two c's, two hundred two d's, one thousand two e's, one hundred eleven h's, two i's, ten l's, one thousand n's, two hundred two o's, one hundred r's, two hundred ten s's, two hundred ten t's, one hundred two u's, ten v's, and one hundred ten w's.

2. This sentence has twenty a's, one b, two c's, one hundred twenty two d's, one thousand twenty two e's, one f, one hundred ten h's, two i's, ten l's, one thousand twenty one n's, two hundred twelve o's, twenty one r's, two hundred twelve s's, one thousand twenty t's, one hundred one u's, ten v's, two hundred w's, and twenty two y's.

3. This sentence has twenty a's, one b, two c's, two hundred one d's, one thousand one hundred two e's, one f, one g, one hundred eleven h's, two i's, one j, twelve l's, one thousand twenty n's, two hundred twenty two o's, twenty two r's, two hundred twelve s's, one thousand ten t's, one hundred two u's, twelve v's, two hundred one w's, and twenty y's.

4. This sentence has twenty one a's, one b, two c's, two hundred eleven d's, one thousand two hundred one e's, one f, one g, one hundred twenty h's, two i's, one j, one k, twelve l's, one m, one thousand one hundred twenty n's, one thousand two o's, one hundred r's, two hundred twenty s's, one thousand t's, one hundred eleven u's, twelve v's, one hundred twenty w's, and twenty one y's.

5. This sentence has twenty one a's, one b, two c's, two hundred eleven d's, one thousand two hundred twelve e's, one f, one g, one hundred twenty h's, two i's, one j, one k, twenty l's, one m, one thousand one hundred twenty two n's, one thousand twelve o's, one p, one q, one hundred r's, two hundred twenty s's, one thousand twelve t's, one hundred eleven u's, twenty v's, two hundred one w's, one x, and twenty two y's.

6. This sentence has twenty one a's, one b, two c's, two hundred eleven d's, one thousand two hundred two e's, one f, one g, one hundred twenty h's, two i's, one j, one k, ten l's, one m, one thousand two hundred two n's, one thousand twenty o's, one p, one q, one hundred r's, two hundred twenty s's, one thousand ten t's, one hundred eleven u's, ten v's, one hundred twenty w's, one x, twenty one y's, and one z.

7. This sentence has twenty one a's, one b, two c's, two hundred eleven d's, one thousand two hundred two e's, one f, one g, one hundred twenty h's, two i's, one j, one k, twelve l's, one thousand one hundred twenty one n's, one thousand ten o's, one hundred r's, two hundred twenty s's, one thousand two t's, one hundred eleven u's, twelve v's, one hundred twenty one w's, and twenty one y's.

8. This sentence has twenty one a's, one b, two c's, two hundred twenty d's, one thousand one hundred twenty two e's, one f, one g, one hundred twenty one h's, two i's, one j, one k, two l's, one m, one thousand two hundred one n's, one thousand one hundred two o's, one p, one q, one hundred one r's, two hundred twenty s's, one thousand twenty two t's, one hundred twelve u's, two v's, two hundred ten w's, and twenty two y's.

9. This sentence has twenty one a's, one b, two c's, two hundred twenty d's, one thousand two hundred one e's, one f, one g, one hundred twenty one h's, two i's, one j, one k, two l's, one m, one thousand two hundred ten n's, one thousand one hundred o's, one p, one q, one hundred one r's, two hundred twenty s's, one thousand ten t's, one hundred twelve u's, two v's, one hundred twenty one w's, and twenty one y's.

10. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred eleven e's, one f, one g, one hundred twelve h's, two i's, one j, twelve l's, one thousand one hundred n's, one thousand o's, twenty two r's, two hundred twenty s's, one thousand two t's, one hundred ten u's, twelve v's, one hundred twenty two w's, and twenty y's.

11. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred twelve e's, one f, one g, one hundred twelve h's, two i's, twelve l's, one thousand one hundred one n's, one thousand o's, twenty two r's, two hundred twenty s's, one thousand one t's, one hundred ten u's, twelve v's, one hundred twenty one w's, and twenty y's.

12. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred twelve e's, one f, one g, one hundred twelve h's, two i's, one j, twelve l's, one thousand one hundred one n's, one thousand o's, twenty two r's, two hundred twenty s's, one thousand ten t's, one hundred ten u's, twelve v's, one hundred twenty two w's, and twenty y's.

13. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred twenty one e's, one f, one g, one hundred twelve h's, two i's, twelve l's, one thousand one hundred ten n's, one thousand o's, twenty two r's, two hundred twenty s's, one thousand eleven t's, one hundred ten u's, twelve v's, one hundred twenty two w's, and twenty one y's.

14. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred twenty one e's, one f, one g, one hundred twelve h's, two i's, one j, one k, ten l's, one m, one thousand one hundred twenty one n's, one thousand twelve o's, twenty two r's, two hundred twenty s's, one thousand twenty two t's, one hundred ten u's, ten v's, two hundred one w's, and twenty two y's.

15. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred twenty two e's, one f, one g, one hundred twelve h's, two i's, one j, one k, eleven l's, one m, one thousand one hundred twenty n's, one thousand ten o's, one p, twenty two r's, two hundred twenty s's, one thousand twenty t's, one hundred ten u's, eleven v's, two hundred w's, and twenty two y's.

16. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred two e's, one f, one g, one hundred twelve h's, two i's, one j, ten l's, one thousand one hundred two n's, one thousand two o's, twenty two r's, two hundred twenty s's, one thousand eleven t's, one hundred ten u's, ten v's, one hundred twenty two w's, and twenty y's.

17. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand one hundred two e's, one f, one g, one hundred twelve h's, two i's, one j, ten l's, one thousand one hundred two n's, one thousand two o's, twenty two r's, two hundred twenty s's, one thousand ten t's, one hundred ten u's, ten v's, one hundred twenty one w's, and twelve y's.

18. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand two hundred e's, one f, one g, one hundred twelve h's, two i's, one j, one k, ten l's, one m, one thousand two hundred n's, one thousand twenty o's, one p, one q, twenty two r's, two hundred twenty s's, one thousand eleven t's, one hundred ten u's, ten v's, one hundred twenty one w's, one x, twenty one y's, and one z.

19. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand two hundred e's, one f, one g, one hundred twelve h's, two i's, one j, one k, twelve l's, one m, one thousand one hundred twelve n's, one thousand twenty o's, one p, one q, twenty two r's, two hundred twenty s's, one thousand twenty t's, one hundred ten u's, twelve v's, two hundred two w's, one x, twenty one y's, and one z.

20. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand two hundred one e's, one f, one g, one hundred twelve h's, two i's, one j, one k, eleven l's, one m, one thousand one hundred twenty two n's, one thousand twenty one o's, one p, one q, twenty two r's, two hundred twenty s's, one thousand twenty t's, one hundred ten u's, eleven v's, two hundred one w's, and twenty two y's.

21. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand two hundred one e's, one f, one g, one hundred twelve h's, two i's, one j, one k, ten l's, one m, one thousand two hundred one n's, one thousand twenty one o's, one p, one q, twenty two r's, two hundred twenty s's, one thousand eleven t's, one hundred ten u's, ten v's, one hundred twenty one w's, and twenty one y's.

22. This sentence has twenty one a's, one b, two c's, two hundred two d's, one thousand two hundred one e's, one f, one g, one hundred twelve h's, two i's, one j, one k, twelve l's, one m, one thousand one hundred twenty n's, one thousand twenty o's, one p, one q, twenty two r's, two hundred twenty s's, one thousand twelve t's, one hundred ten u's, twelve v's, two hundred one w's, one x, and twenty one y's.

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