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: Decimal Digits

Self-referential ``this sentence has'' sentences with ordinary numerals, exhaustive list - there are no others.


1. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 19 s's, 3 t's, 2 1's, 6 2's, 6 3's, 3 4's, 3 6's, and 2 9's.

2. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 19 s's, 3 t's, 1 0, 5 1's, 5 2's, 4 3's, 5 4's, 4 5's, 1 6, 1 7, and 2 9's.

3. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 19 s's, 3 t's, 1 0, 5 1's, 5 2's, 5 3's, 3 4's, 5 5's, 1 6, 1 7, and 2 9's.

4. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 2 1's, 9 2's, 5 3's, 3 4's, 2 5's, 1 6, and 2 9's.

5. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 3 1's, 8 2's, 5 3's, 4 4's, 2 5's, 1 6, 1 7, and 2 8's.

6. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 3 1's, 8 2's, 6 3's, 3 4's, 1 5, 2 6's, 1 7, and 2 8's.

7. This sentence has 3 a's, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 4 1's, 8 2's, 4 3's, 5 4's, 2 5's, 1 6, 1 7, 2 8's, and 1 9.

8. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 5 1's, 7 2's, 5 3's, 4 4's, 3 5's, 1 6, 2 7's, 1 8, and 1 9.

9. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 6 1's, 7 2's, 6 3's, 3 4's, 1 5, 3 6's, 2 7's, 1 8, and 1 9.

10. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 4 n's, 19 s's, 3 t's, 1 0, 11 1's, 5 2's, 5 3's, 4 4's, 3 5's, 1 6, 1 7, 1 8, and 2 9's.

11. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 7 1's, 7 2's, 5 3's, 4 4's, 2 5's, 1 6, 3 7's, 1 8, and 1 9.

12. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 4 n's, 20 s's, 3 t's, 2 0's, 7 1's, 7 2's, 6 3's, 3 4's, 1 5, 2 6's, 3 7's, 1 8, and 1 9.

13. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 4 n's, 19 s's, 3 t's, 1 0, 12 1's, 6 2's, 6 3's, 3 4's, 1 5, 3 6's, 1 7, 1 8, and 2 9's.

14. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 4 n's, 20 s's, 3 t's, 2 0's, 11 1's, 8 2's, 5 3's, 3 4's, 2 5's, 1 6, 1 7, 2 8's, and 1 9.

15. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 4 n's, 20 s's, 3 t's, 3 0's, 10 1's, 7 2's, 5 3's, 4 4's, 2 5's, 1 6, 2 7's, 1 8, and 1 9.

16. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 4 n's, 20 s's, 3 t's, 3 0's, 10 1's, 7 2's, 6 3's, 3 4's, 1 5, 2 6's, 2 7's, 1 8, and 1 9.

17. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 20 s's, 3 t's, 2 0's, 12 1's, 9 2's, 5 3's, 3 4's, 2 5's, 1 6, 1 7, 1 8, and 2 9's.

18. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 19 s's, 3 t's, 1 0, 15 1's, 5 2's, 4 3's, 5 4's, 4 5's, 1 6, 1 7, 1 8, and 2 9's.

19. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 19 s's, 3 t's, 1 0, 15 1's, 5 2's, 5 3's, 3 4's, 5 5's, 1 6, 1 7, 1 8, and 2 9's.

20. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 20 s's, 3 t's, 2 0's, 13 1's, 8 2's, 5 3's, 4 4's, 2 5's, 1 6, 1 7, 2 8's, and 1 9.

21. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 20 s's, 3 t's, 2 0's, 13 1's, 8 2's, 6 3's, 3 4's, 1 5, 2 6's, 1 7, 2 8's, and 1 9.

22. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 20 s's, 3 t's, 2 0's, 14 1's, 8 2's, 4 3's, 5 4's, 2 5's, 1 6, 1 7, 2 8's, and 1 9.

23. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 20 s's, 3 t's, 2 0's, 15 1's, 7 2's, 5 3's, 4 4's, 3 5's, 1 6, 2 7's, 1 8, and 1 9.

24. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 19 s's, 3 t's, 1 u, 1 v, 1 w, 1 0, 21 1's, 6 2's, 6 3's, 3 4's, 1 5, 3 6's, 1 7, 1 8, and 2 9's.

25. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 19 s's, 3 t's, 1 u, 1 v, 1 w, 1 x, 1 y, 1 z, 1 0, 23 1's, 6 2's, 6 3's, 4 4's, 1 5, 3 6's, 1 7, 1 8, and 2 9's.

26. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 20 s's, 3 t's, 2 0's, 16 1's, 7 2's, 6 3's, 3 4's, 1 5, 3 6's, 2 7's, 1 8, and 1 9.

27. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 20 s's, 3 t's, 1 u, 2 0's, 17 1's, 7 2's, 5 3's, 4 4's, 2 5's, 1 6, 3 7's, 1 8, and 1 9.

28. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 20 s's, 3 t's, 1 u, 2 0's, 17 1's, 7 2's, 6 3's, 3 4's, 1 5, 2 6's, 3 7's, 1 8, and 1 9.

29. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 20 s's, 3 t's, 1 u, 1 v, 1 w, 1 x, 1 y, 2 0's, 21 1's, 9 2's, 5 3's, 3 4's, 2 5's, 1 6, 1 7, 1 8, and 2 9's.

30. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 20 s's, 3 t's, 1 u, 1 v, 1 w, 1 x, 1 y, 3 0's, 20 1's, 8 2's, 5 3's, 4 4's, 2 5's, 1 6, 1 7, 2 8's, and 1 9.

31. This sentence has 3 a's, 1 b, 2 c's, 2 d's, 4 e's, 1 f, 1 g, 3 h's, 2 i's, 1 j, 1 k, 1 l, 1 m, 4 n's, 1 o, 1 p, 1 q, 1 r, 20 s's, 3 t's, 1 u, 1 v, 1 w, 1 x, 1 y, 3 0's, 20 1's, 8 2's, 6 3's, 3 4's, 1 5, 2 6's, 1 7, 2 8's, and 1 9.

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