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 100

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


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

2. A hundred bottles of beer, four a's, three b's, one c, four d's, thirty e's, ten f's, one g, seven h's, five i's, four l's, sixteen n's, fourteen o's, fourteen r's, twenty three s's, seventeen t's, nine u's, four v's, four w's, two x's, and three y's on the wall.

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

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

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

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

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

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

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

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

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

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