Self Referential Sentences

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


1. This sentence has three a's, two c's, two d's, nineteen e's, six f's, two g's, five h's, ten i's, two l's, twelve n's, nine o's, five r's, twenty six s's, sixteen t's, four u's, four v's, eight w's, four x's, and two y's.

2. This sentence has three a's, two c's, two d's, twenty eight e's, four f's, four g's, ten h's, eight i's, two l's, eleven n's, six o's, seven r's, twenty seven s's, eighteen t's, three u's, five v's, six w's, three x's, and three y's.

3. This sentence has three a's, two c's, two d's, twenty six e's, three f's, three g's, eleven h's, eight i's, two l's, thirteen n's, eight o's, nine r's, twenty four s's, twenty three t's, three u's, two v's, nine w's, two x's, and four y's.

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

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

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

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

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

9. This sentence has three a's, one b, two c's, two d's, thirty two e's, three f's, one g, seven h's, seven i's, one j, one k, one l, nineteen n's, ten o's, five r's, twenty five s's, seventeen t's, seven v's, six w's, two x's, and three y's.

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

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

12. This sentence has three a's, one b, two c's, two d's, twenty five e's, five f's, one g, seven h's, thirteen i's, one j, thirteen n's, six o's, five r's, twenty six s's, sixteen t's, six v's, five w's, six x's, and three y's.

13. This sentence has three a's, one b, two c's, two d's, twenty four e's, five f's, one g, six h's, ten i's, thirteen n's, seven o's, five 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.

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

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

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

17. This sentence has three a's, one b, two c's, two d's, twenty six e's, five f's, one g, five h's, ten i's, one j, one k, one l, sixteen n's, ten o's, four r's, twenty seven s's, sixteen t's, two u's, five v's, six w's, six x's, and three y's.

18. This sentence has three a's, one b, two c's, two d's, twenty six e's, five f's, three g's, nine h's, eleven i's, one j, two l's, thirteen n's, eight o's, six r's, twenty five s's, twenty t's, two u's, five v's, eight w's, three x's, and four y's.

Self-Referential Sentences: Base Ten

Self-referential ``this sentence makes use of'' sentences in decimal, exhaustive list - there are no others.


1. This sentence makes use of three a's, two c's, two d's, twenty eight e's, six f's, five g's, nine h's, eleven i's, two k's, three l's, two m's, eleven n's, eight o's, six r's, twenty eight s's, twenty t's, four u's, five v's, eight w's, three x's, and four y's.

2. This sentence makes use of three a's, one b, two c's, two d's, thirty one e's, five f's, two g's, seven h's, eight i's, one j, two k's, one l, two m's, seventeen n's, fourteen o's, seven r's, thirty s's, nineteen t's, four u's, six v's, seven w's, two x's, and three y's.

3. This sentence makes use of three a's, one b, two c's, two d's, twenty five e's, seven f's, two g's, six h's, nine i's, two k's, two m's, fifteen n's, ten o's, six r's, twenty eight s's, twenty t's, four u's, three v's, nine w's, three x's, and four y's.

4. This sentence makes use of three a's, one b, two c's, two d's, twenty six e's, ten f's, two g's, four h's, eight i's, one j, two k's, two m's, fifteen n's, fourteen o's, five r's, twenty seven s's, twenty one t's, five u's, five v's, ten w's, two x's, and four y's.

Self-Referential Sentences: Base Ten

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


1. This sentence employs two a's, two c's, two d's, twenty one e's, six f's, two g's, four h's, seven i's, four l's, two m's, ten n's, twelve o's, two p's, five r's, twenty eight s's, twenty t's, four u's, six v's, twelve w's, three x's, and five y's.

2. This sentence employs two a's, two c's, two d's, twenty six e's, four f's, two g's, seven h's, nine i's, three l's, two m's, thirteen n's, ten o's, two p's, six r's, twenty eight s's, twenty three t's, two u's, five v's, eleven w's, three x's, and five y's.

3. This sentence employs two a's, one b, two c's, two d's, thirty three e's, three f's, two g's, seven h's, seven i's, one j, one k, three l's, two m's, seventeen n's, eleven o's, two p's, five r's, twenty seven s's, twenty t's, eight v's, nine w's, and five y's.

4. This sentence employs two a's, one b, two c's, two d's, twenty eight e's, five f's, three g's, eight h's, eleven i's, three l's, two m's, thirteen n's, nine o's, two p's, five r's, twenty five s's, twenty three t's, six v's, ten w's, two x's, and five y's.

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

Self-Referential Sentences: Base Ten

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


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

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

3. This sentence consists of two a's, one b, three c's, two d's, twenty five e's, seven f's, two g's, six h's, nine i's, one j, two l's, fifteen n's, twelve o's, six r's, twenty eight s's, twenty two t's, three u's, four v's, ten w's, three x's, and four y's.

4. This sentence consists of two a's, one b, three c's, two d's, twenty five e's, six f's, two g's, six h's, thirteen i's, sixteen n's, nine o's, five r's, twenty eight s's, nineteen t's, two u's, five v's, seven w's, four x's, and three y's.

5. This sentence consists of two a's, one b, three c's, two d's, twenty nine e's, five f's, two g's, seven h's, thirteen i's, one j, nineteen n's, eight o's, five r's, twenty six s's, nineteen t's, five v's, six w's, three x's, and three y's.

6. This sentence consists of two a's, one b, three c's, two d's, twenty two e's, seven f's, two g's, five h's, eight i's, fourteen n's, thirteen o's, six r's, twenty seven s's, twenty two t's, four u's, five v's, ten w's, two x's, and four y's.

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.

Self-Referential Sentences: Base Ten

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


1. This sentence incorporates three a's, three c's, two d's, thirty e's, four f's, three g's, eleven h's, eight i's, three l's, ten n's, eight o's, two p's, twelve 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.

2. This sentence incorporates three a's, three c's, two d's, twenty eight e's, five f's, three g's, eight h's, ten i's, sixteen n's, nine o's, two p's, nine r's, twenty five s's, twenty one t's, three u's, four v's, seven w's, two x's, and four y's.

3. This sentence incorporates three a's, three c's, two d's, twenty six e's, three f's, two g's, eight h's, ten i's, sixteen n's, nine o's, two p's, nine r's, twenty five s's, twenty three t's, two u's, two v's, nine w's, three x's, and four y's.

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

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

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

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

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

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

10. This sentence incorporates three a's, one b, three c's, two d's, thirty three e's, three f's, two g's, ten h's, eight i's, one j, one k, two l's, seventeen n's, thirteen o's, two p's, twelve r's, twenty seven s's, twenty six t's, three u's, four v's, nine w's, two x's, and four y's.

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

12. This sentence incorporates three a's, one b, three c's, two d's, twenty six e's, four f's, two g's, seven h's, nine i's, one j, eighteen n's, thirteen o's, two p's, ten r's, twenty six s's, twenty two t's, four u's, two v's, nine w's, three x's, and four y's.

Self-Referential Sentences: Base Ten

Self-referential ``this sentence is composed of'' sentences in decimal, exhaustive list - there are no others.


1. This sentence is composed of two a's, three c's, three d's, twenty five e's, seven f's, two g's, six h's, nine i's, two m's, fourteen n's, thirteen o's, two p's, seven r's, twenty eight s's, twenty two t's, four u's, five v's, ten w's, two x's, and four y's.

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

3. This sentence is composed of two a's, one b, three c's, three d's, thirty three e's, eight f's, three g's, eleven h's, thirteen i's, one j, one k, two l's, two m's, fifteen n's, thirteen o's, two p's, nine r's, twenty five s's, twenty five t's, two u's, five v's, eight w's, and four y's.

4. This sentence is composed of two a's, one b, three c's, three d's, thirty three e's, seven f's, three g's, ten h's, eight i's, one j, one k, one l, two m's, sixteen n's, fifteen o's, two p's, ten r's, twenty eight s's, twenty four t's, four u's, three v's, seven w's, two x's, and four y's.

5. This sentence is composed of two a's, one b, three c's, three d's, twenty six e's, six f's, one g, six h's, eleven i's, two l's, two m's, fifteen n's, thirteen o's, two p's, six r's, twenty nine s's, twenty two t's, two u's, three v's, ten w's, five x's, and four y's.

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