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 ``in this sentence there are'' sentences in decimal, exhaustive list - there are no others.


1. In this sentence there are three a's, two c's, two d's, twenty six e's, four f's, six h's, ten i's, thirteen n's, five o's, seven r's, twenty seven s's, seventeen t's, two u's, six v's, six w's, five x's, and three y's.

2. In this sentence there are three a's, one b, two c's, two d's, thirty e's, four f's, two g's, nine h's, eight i's, one j, one k, three l's, sixteen n's, twelve o's, eleven r's, twenty three s's, twenty two t's, four u's, three v's, nine w's, two x's, and four y's.

3. In this sentence there are three a's, one b, two c's, two d's, thirty four e's, five f's, one g, seven h's, seven i's, one j, one k, one l, twenty n's, ten o's, nine r's, twenty three s's, seventeen t's, three u's, seven v's, five w's, and four y's.

4. In this sentence there are three a's, one b, two c's, two d's, thirty three e's, four f's, two g's, nine h's, seven i's, one j, one k, two l's, seventeen n's, eleven o's, ten r's, twenty three s's, twenty two t's, three u's, five v's, eight w's, and four y's.

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

6. In this sentence there are three a's, one b, two c's, two d's, thirty two e's, four f's, one g, seven h's, nine i's, one j, one k, one l, one m, twenty four n's, sixteen o's, one p, nine r's, twenty two s's, twenty one t's, three u's, three v's, nine w's, two x's, and five y's.

7. In this sentence there are three a's, one b, two c's, two d's, twenty five e's, six f's, three g's, seven h's, eight i's, two l's, twelve n's, ten o's, eight r's, twenty four s's, twenty two t's, four u's, five v's, ten w's, two x's, and four y's.

8. In this sentence there are three a's, one b, two c's, two d's, twenty nine e's, four f's, one g, five h's, ten i's, seventeen n's, seven o's, six r's, twenty seven s's, sixteen t's, two u's, six v's, six w's, five x's, and three y's.

9. In this sentence there are three a's, one b, two c's, two d's, twenty nine e's, six f's, one g, five h's, twelve i's, two l's, fifteen n's, six o's, five r's, twenty six s's, sixteen t's, seven v's, seven w's, five x's, and three y's.

10. In this sentence there are three a's, one b, two c's, two d's, twenty nine e's, three f's, one g, six h's, seven i's, one j, one k, twenty n's, ten o's, seven r's, twenty three s's, twenty t's, two u's, four v's, nine w's, two x's, and five y's.

11. In this sentence there are three a's, one b, two c's, two d's, twenty six e's, four f's, three g's, eight h's, nine i's, seventeen n's, nine o's, nine r's, twenty three s's, twenty t's, four u's, two v's, eight w's, two x's, and four y's.

12. In this sentence there are three a's, one b, two c's, two d's, twenty six e's, two f's, one g, six h's, nine i's, twenty n's, nine o's, seven r's, twenty three s's, nineteen t's, two u's, two v's, nine w's, three x's, and four y's.

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