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: Beer 98

Self-referential ``Ninety eight bottles of beer'' sentences, exhaustive list - there are no others.


1. Ninety eight bottles of beer, three a's, three b's, two d's, twenty nine e's, eight f's, four g's, seven h's, ten i's, four l's, nineteen n's, ten o's, eight r's, twenty one s's, nineteen t's, five u's, four v's, five w's, and four y's on the wall.

2. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty eight e's, eight f's, four g's, ten h's, eleven i's, one j, one k, five l's, one m, twenty one n's, fifteen o's, one p, one q, nine r's, twenty three s's, twenty four t's, three u's, five v's, seven w's, two x's, and six y's on the wall.

3. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty five e's, seven f's, four g's, nine h's, eleven i's, one j, five l's, eighteen n's, ten o's, eight r's, twenty two s's, nineteen t's, three u's, seven v's, five w's, and four y's on the wall.

4. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty five e's, seven f's, three g's, eight h's, fifteen i's, one j, one k, five l's, one m, nineteen n's, twelve o's, one p, one q, six r's, twenty six s's, twenty t's, one u, six v's, six w's, six x's, and five y's on the wall.

5. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty four e's, six f's, three g's, nine h's, eleven i's, one j, five l's, sixteen n's, ten o's, eight r's, twenty five s's, twenty two t's, two u's, seven v's, seven w's, three x's, and five y's on the wall.

6. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty four e's, six f's, three g's, nine h's, twelve i's, one j, one k, six l's, one m, seventeen n's, twelve o's, nine r's, twenty five s's, twenty two t's, three u's, six v's, eight w's, four x's, and five y's on the wall.

7. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty one e's, seven f's, three g's, eight h's, eleven i's, one j, five l's, fifteen n's, ten o's, seven r's, twenty six s's, twenty t's, two u's, six v's, six w's, four x's, and five y's on the wall.

8. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty one e's, seven f's, three g's, nine h's, nine i's, one j, one k, four l's, one m, twenty n's, fifteen o's, ten r's, twenty three s's, twenty four t's, four u's, two v's, eight w's, two x's, and six y's on the wall.

9. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty seven e's, five f's, three g's, eleven h's, thirteen i's, one j, one k, five l's, eighteen n's, nine o's, nine r's, twenty three s's, twenty two t's, six v's, six w's, three x's, and five y's on the wall.

10. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty six e's, six f's, three g's, ten h's, thirteen i's, one j, one k, five l's, one m, eighteen n's, twelve o's, one p, nine r's, twenty five s's, twenty three t's, two u's, six v's, seven w's, four x's, and five y's on the wall.

11. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty three e's, eight f's, four g's, ten h's, eleven i's, one j, one k, six l's, fifteen n's, twelve o's, nine r's, twenty two s's, twenty four t's, three u's, five v's, eight w's, two x's, and five y's on the wall.

12. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty three e's, six f's, three g's, nine h's, fourteen i's, one j, one k, five l's, sixteen n's, eleven o's, eight r's, twenty six s's, twenty one t's, two u's, five v's, six w's, six x's, and five y's on the wall.

13. Ninety eight bottles of beer, three a's, three b's, one c, two d's, thirty two e's, eight f's, five g's, ten h's, thirteen i's, one j, one k, four l's, one m, eighteen n's, sixteen o's, one p, nine r's, twenty two s's, twenty five t's, four u's, four v's, eight w's, two x's, and five y's on the wall.

14. Ninety eight bottles of beer, three a's, three b's, one c, two d's, twenty four e's, six f's, two g's, five h's, twelve i's, six l's, twelve n's, nine o's, five r's, twenty six s's, twenty t's, two u's, six v's, ten w's, six x's, and five y's on the wall.

15. Ninety eight bottles of beer, three a's, three b's, one c, two d's, twenty nine e's, four f's, three g's, nine h's, nine i's, four l's, twenty n's, ten o's, nine r's, twenty one s's, twenty three t's, three u's, eight w's, two x's, and six y's on the wall.

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