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 Nine

Self-referential ``this sentence has'' sentences in base nine, exhaustive list - there are no others.


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

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

3. This sentence has three a's, one b, two c's, two d's, forty e's, five f's, three g's, eight h's, eight 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 seven s's, twenty one t's, one u, seven v's, seven w's, two x's, five y's, and one z.

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

5. This sentence has three a's, one b, two c's, two d's, thirty five e's, seven f's, three g's, ten h's, eleven i's, one j, one k, two l's, fifteen n's, seven o's, five r's, twenty five s's, eighteen t's, eight v's, five w'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, seven h's, seven i's, one j, one k, one l, twenty n's, thirteen o's, five r's, twenty seven s's, twenty one t's, two u's, seven v's, eight w's, and five y's.

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

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

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

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