Search: keyword:precise
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| BP956 |
| Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets). |
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COMMENTS
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Examples on the left are also known as "Dyck words". |
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REFERENCE
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https://en.wikipedia.org/wiki/Dyck_language |
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CROSSREFS
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Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955 * BP957 BP958 BP959 BP960 BP961
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KEYWORD
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easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable
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CONCEPT
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recursion (info | search)
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AUTHOR
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Aaron David Fairbanks
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| BP961 |
| Includes itself on the left vs. includes itself on the right. |
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COMMENTS
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Some examples are Bongard Problems with this solution. |
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CROSSREFS
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Adjacent-numbered pages:
BP956 BP957 BP958 BP959 BP960 * BP962 BP963 BP964 BP965 BP966
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KEYWORD
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nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld
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CONCEPT
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fractal (info | search),
recursion (info | search),
self-reference (info | search)
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AUTHOR
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Aaron David Fairbanks
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CROSSREFS
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Adjacent-numbered pages:
BP957 BP958 BP959 BP960 BP961 * BP963 BP964 BP965 BP966 BP967
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KEYWORD
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precise, allsorted, minimal, dual, blackwhite, gap, left-finite, right-finite, left-full, right-full, left-null, finished, preciseworld, unstableworld
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WORLD
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[smaller | same | bigger]
zoom in left (blank_image) | zoom in right (black_image)
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AUTHOR
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Leo Crabbe
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| BP965 |
| If you place the image on top of itself so that it lines up with itself exactly within a small region, it also lines up everywhere else vs. not so. |
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COMMENTS
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Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.
Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about. |
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CROSSREFS
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See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.
Adjacent-numbered pages:
BP960 BP961 BP962 BP963 BP964 * BP966 BP967 BP968 BP969 BP970
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KEYWORD
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hard, precise, distractingworld, perfect
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CONCEPT
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local_global (info | search)
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AUTHOR
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Aaron David Fairbanks
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| BP971 |
| Left half has more black (less white) than right half versus vice versa. |
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COMMENTS
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A similar, but different, solution is "center of mass is on the left half vs. center of mass is on the right half." |
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CROSSREFS
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See BP972 for the version with examples rotated a quarter-turn.
Adjacent-numbered pages:
BP966 BP967 BP968 BP969 BP970 * BP972 BP973 BP974 BP975 BP976
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KEYWORD
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nice, precise, spectrum, dual, handed, leftright, rotate, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent
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AUTHOR
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Aaron David Fairbanks
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| BP972 |
| Top half has more black (less white) than bottom half versus vice versa. |
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COMMENTS
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A similar, but different, solution is "center of mass is above the horizontal vs. center of mass is below the horizontal." |
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CROSSREFS
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See BP971 for the version with examples rotated a quarter-turn.
Adjacent-numbered pages:
BP967 BP968 BP969 BP970 BP971 * BP973 BP974 BP975 BP976 BP977
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KEYWORD
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precise, spectrum, dual, handed, updown, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent
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AUTHOR
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Aaron David Fairbanks
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| BP977 |
| Two of the same object are enclosed in the same space (there is a path between them) vs. not so. |
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| BP986 |
| Palindromes vs. not palindromes. |
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COMMENTS
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All examples in this Problem are sequences of graphic symbols. In this Problem, a "palindrome" is taken to be an ordered sequence which is the same read left-to-right as it is read right-to-left. A more formal solution to this Problem could be: "Sequences which are invariant under a permutation which swaps first and last entries, second and second last entries, third and third last entries, ... and so on vs. sequences which are not invariant under the aforementioned permutamation." |
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CROSSREFS
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Adjacent-numbered pages:
BP981 BP982 BP983 BP984 BP985 * BP987 BP988 BP989 BP990 BP991
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KEYWORD
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nice, precise, allsorted, notso, sequence, traditional
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CONCEPT
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element_wise_symmetry (info | search),
identical (info | search),
sequence (info | search),
same_shape (info | search),
same (info | search),
symmetry (info | search)
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WORLD
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zoom in left | zoom in right
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AUTHOR
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Jago Collins
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