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


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

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

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

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

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

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

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

8. This sentence includes two a's, one b, three c's, three d's, thirty two e's, three f's, two g's, eleven h's, eight i's, three l's, thirteen n's, seven o's, ten 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.

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

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