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 incorporates'' sentences in decimal, exhaustive list - there are no others.


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

2. This sentence incorporates three a's, three c's, two d's, twenty eight e's, five f's, three g's, eight h's, ten i's, sixteen n's, nine o's, two p's, nine r's, twenty five s's, twenty one t's, three u's, four v's, seven w's, two x's, and four y's.

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

4. This sentence incorporates three a's, one b, three c's, two d's, thirty e's, four f's, one g, seven h's, nine i's, two l's, nineteen n's, eleven o's, two p's, ten r's, twenty five s's, nineteen t's, three u's, four v's, six w's, two x's, and three y's.

5. This sentence incorporates three a's, one b, three c's, two d's, thirty e's, four f's, one g, seven h's, nine i's, one j, one k, one l, twenty one n's, thirteen o's, two p's, nine r's, twenty three s's, twenty t's, two u's, five v's, seven w's, and five y's.

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

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

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

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

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

11. This sentence incorporates three a's, one b, three c's, two d's, thirty two e's, three f's, two g's, ten h's, nine i's, one j, one k, two l's, eighteen n's, thirteen o's, two p's, eleven r's, twenty three s's, twenty five t's, two u's, three v's, nine w's, and four y's.

12. This sentence incorporates three a's, one b, three c's, two d's, twenty six e's, four f's, two g's, seven h's, nine i's, one j, eighteen n's, thirteen o's, two p's, ten r's, twenty six s's, twenty two t's, four u's, two v's, nine w's, three x's, and four y's.

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