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 Ten

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


1. This sentence has three a's, two c's, two d's, nineteen e's, six f's, two g's, five h's, ten i's, two l's, twelve n's, nine o's, five r's, twenty six s's, sixteen t's, four u's, four v's, eight w's, four x's, and two y's.

2. This sentence has three a's, two c's, two d's, twenty eight e's, four f's, four g's, ten h's, eight i's, two l's, eleven n's, six o's, seven r's, twenty seven s's, eighteen t's, three u's, five v's, six w's, three x's, and three y's.

3. This sentence has three a's, two c's, two d's, twenty six e's, three f's, three g's, eleven h's, eight i's, two l's, thirteen n's, eight o's, nine r's, twenty four s's, twenty three t's, three u's, two v's, nine w's, two x's, and four y's.

4. This sentence has three a's, one b, two c's, two d's, thirty e's, five f's, three g's, ten h's, seven i's, one j, one k, two l's, one m, fourteen n's, twelve o's, one p, eight r's, twenty three s's, twenty two t's, three u's, five v's, eight w's, and four y's.

5. This sentence has three a's, one b, two c's, two d's, thirty e's, three f's, one g, seven h's, nine i's, one j, one k, two l's, one m, nineteen n's, eleven o's, six r's, twenty seven s's, sixteen t's, two u's, five v's, six w's, four x's, and three y's.

6. This sentence has three a's, one b, two c's, two d's, thirty one e's, four f's, two g's, nine h's, nine i's, one j, one k, one l, one m, twenty three n's, sixteen o's, one p, one q, nine r's, twenty three s's, eighteen t's, four u's, one v, six w's, three x's, and four y's.

7. This sentence has three a's, one b, two c's, two d's, thirty one e's, seven f's, one g, six h's, seven i's, one j, one k, one l, one m, twenty n's, fourteen o's, one p, seven r's, twenty seven s's, fifteen t's, four u's, six v's, five w's, three x's, and four y's.

8. This sentence has three a's, one b, two c's, two d's, thirty six e's, three f's, three g's, eleven h's, nine i's, one j, one k, three l's, one m, eighteen n's, twelve o's, one p, one q, eight r's, twenty six s's, twenty t's, two u's, five v's, seven w's, three x's, four y's, and one z.

9. This sentence has three a's, one b, two c's, two d's, thirty two e's, three f's, one g, seven h's, seven i's, one j, one k, one l, nineteen n's, ten o's, five r's, twenty five s's, seventeen t's, seven v's, six w's, two x's, and three y's.

10. This sentence has three a's, one b, two c's, two d's, thirty two e's, three f's, two g's, eleven h's, seven i's, one j, one k, two l's, one m, sixteen n's, thirteen o's, one p, ten r's, twenty six s's, twenty four t's, three u's, three v's, eight w's, three x's, and four y's.

11. This sentence has three a's, one b, two c's, two d's, twenty five e's, eight f's, two g's, six h's, nine i's, one j, one k, two l's, one m, fifteen n's, twelve o's, five r's, twenty four s's, twenty t's, three u's, five v's, ten w's, two x's, and four y's.

12. This sentence has three a's, one b, two c's, two d's, twenty five e's, five f's, one g, seven h's, thirteen i's, one j, thirteen n's, six o's, five r's, twenty six s's, sixteen t's, six v's, five w's, six x's, and three y's.

13. This sentence has three a's, one b, two c's, two d's, twenty four e's, five f's, one g, six h's, ten i's, thirteen n's, seven o's, five r's, twenty seven s's, sixteen t's, two u's, six v's, six w's, five x's, and three y's.

14. This sentence has three a's, one b, two c's, two d's, twenty nine e's, five f's, one g, six h's, ten i's, one j, one k, one l, one m, twenty one n's, thirteen o's, one p, six r's, twenty six s's, seventeen t's, three u's, four v's, six w's, five x's, and four y's.

15. This sentence has three a's, one b, two c's, two d's, twenty nine e's, seven f's, two g's, five h's, nine i's, one j, one k, one l, one m, twenty one n's, fourteen o's, five r's, twenty five s's, seventeen t's, four u's, six v's, eight w's, two x's, and four y's.

16. This sentence has three a's, one b, two c's, two d's, twenty nine e's, two f's, three g's, nine h's, eight i's, sixteen n's, seven o's, six r's, twenty seven s's, eighteen t's, two u's, four v's, seven w's, three x's, and three y's.

17. This sentence has three a's, one b, two c's, two d's, twenty six e's, five f's, one g, five h's, ten i's, one j, one k, one l, sixteen n's, ten o's, four r's, twenty seven s's, sixteen t's, two u's, five v's, six w's, six x's, and three y's.

18. This sentence has three a's, one b, two c's, two d's, twenty six e's, five f's, three g's, nine h's, eleven i's, one j, two l's, thirteen n's, eight o's, six r's, twenty five s's, twenty t's, two u's, five v's, eight w's, three x's, and four y's.

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