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 99

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


1. Ninety nine 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, eighteen t's, five u's, four v's, five w's, and four y's on the wall.

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

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

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

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

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

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

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

9. Ninety nine 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, eighteen t's, three u's, seven v's, five w's, and four y's on the wall.

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

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

12. Ninety nine bottles of beer, three a's, three b's, one c, two d's, thirty seven e's, five f's, three g's, ten h's, eleven i's, one j, one k, five l's, one m, eighteen n's, ten o's, eight 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.

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

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

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

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