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: Binary Beads

Self-referential ``this sentence has'' sentences with binary beads at a bead a letter, a is 1, b is 2, c is 4, d is 8, ..., exhaustive list - there are no others.


1. This sentence has abc a's, abc b's, d c's, c d's, c e's, ab h's, b i's, c n's, bcd s's, and ab t's.

2. This sentence has abcd a's, abc b's, d c's, ac d's, c e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, bcd s's, and ab t's.

3. This sentence has abce a's, abc b's, d c's, c d's, ac e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, a p, a q, a r, bcd s's, ab t's, a u, a v, a w, a x, and a y.

4. This sentence has acd a's, ac b's, d c's, ac d's, c e's, a f, a g, ab h's, b i's, a j, a k, a l, c n's, bcd s's, and ab t's.

5. This sentence has acd a's, bc b's, d c's, ac d's, c e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, bcd s's, and ab t's.

6. This sentence has ace a's, ac b's, d c's, c d's, ac e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, a p, a q, a r, bcd s's, ab t's, a u, a v, and a w.

7. This sentence has ace a's, bc b's, d c's, c d's, ac e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, a p, a q, a r, bcd s's, ab t's, a u, a v, a w, and a x.

8. This sentence has bc a's, abc b's, d c's, c d's, c e's, ab h's, b i's, c n's, bcd s's, and ab t's.

9. This sentence has bcd a's, abc b's, d c's, ac d's, c e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, bcd s's, and ab t's.

10. This sentence has bce a's, abc b's, d c's, c d's, ac e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, a p, a q, a r, bcd s's, ab t's, a u, a v, a w, a x, and a y.

11. This sentence has cd a's, ac b's, d c's, ac d's, c e's, a f, a g, ab h's, b i's, a j, a k, a l, c n's, bcd s's, and ab t's.

12. This sentence has cd a's, bc b's, d c's, ac d's, c e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, bcd s's, and ab t's.

13. This sentence has ce a's, ac b's, d c's, c d's, ac e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, a p, a q, a r, bcd s's, ab t's, a u, a v, and a w.

14. This sentence has ce a's, bc b's, d c's, c d's, ac e's, a f, a g, ab h's, b i's, a j, a k, a l, a m, c n's, a o, a p, a q, a r, bcd s's, ab t's, a u, a v, a w, and a x.

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