Search: all:new
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| BP989 |
| Number of dots is n factorial for some n vs. not so. |
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| BP988 |
| Number of dots is a power of 2 vs. not so. |
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| BP987 |
| Solution could appear in a Bongard Problem featuring an image of itself on either of its sides vs. solution can appear in a Bongard Problem featuring an image of itself on a certain side only. |
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COMMENTS
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All examples are Bongard Problems fitting left in BP954.
This is very close to BP927, specialized to Bongard Problems fitting left in BP954. The difference is that a Bongard Problem solution would fit left in BP927 but right here if it can sort images of it on both sides, but it is impossible to make an image of it fractally including itself on a certain side. An example is EX7997.
Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit right here. |
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CROSSREFS
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Adjacent-numbered pages:
BP982 BP983 BP984 BP985 BP986 * BP988 BP989 BP990 BP991 BP992
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KEYWORD
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abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant, visualimagination
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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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Leo Crabbe
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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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| BP985 |
| Bongard Problem with solution relating to concept: perpendicular vs. Bongard Problem unrelated to this concept. |
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| BP984 |
| Bongard Problem with solution relating to concept: parallel vs. Bongard Problem unrelated to this concept. |
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| BP983 |
| Bongard Problem with solution relating to concept: comparison of multiple quantities (within one example) vs. Bongard Problem unrelated to this concept. |
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COMMENTS
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"More," "fewer," "greater than," "less than."
See BP752 and BP749 for equality. |
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CROSSREFS
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Adjacent-numbered pages:
BP978 BP979 BP980 BP981 BP982 * BP984 BP985 BP986 BP987 BP988
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KEYWORD
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meta (see left/right), links, metaconcept
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CONCEPT
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This MBP is about BPs that feature concept: "quantity_comparison"
Searchable synonyms: "more", "less", "greater", "lesser", "greater than", "less than", "fewer".
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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| BP982 |
| Bongard Problem with solution relating to concept: most extreme thing in some way out of multiple things vs. Bongard Problem unrelated to this concept. |
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| BP981 |
| Grid of analogies vs. different kind of rule. |
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COMMENTS
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On the left, each row and column could be labeled by a certain object or concept; on the right this is not so.
More specifically: on the left, each row and each column is associated with a certain object or concept; there is a rule for combining rows and columns to give images; it would be possible without changing the rule to extend with new rows/columns or delete/reorder any existing columns. On the right, this is not so; the rule might be about how the images must relate to their neighbors, for example.
All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey.
Left examples are a generalized version of the analogy grids seen in BP361. Any analogy a : b :: c : d shown in a 2x2 grid will fit on the left here.
To word the solution with mathematical jargon, "defines a (simply described) map from the Cartesian product of two sets vs. not so." Another equivalent solution is "columns (alternatively, rows) illustrate a consistent set of one-input operations." It is always possible to imagine the columns as inputs and the rows as operations and vice versa.
There is a trivial way in which any example can be interpreted so that it fits on the left side: imagine each row is assigned the list of all the squares in that row and each column is assigned its number, counting from the left. But each grid has a clear rule that is simpler than this. |
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CROSSREFS
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BP1258 is a similar idea: "any square removed could be reconstructed vs. not." Examples included left here usually fit left there, but some do not e.g. EX9998.
See BP979 for use of similar structures but with one square removed from the grid.
Adjacent-numbered pages:
BP976 BP977 BP978 BP979 BP980 * BP982 BP983 BP984 BP985 BP986
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KEYWORD
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nice, convoluted, unwordable, notso, teach, structure, rules, grid, miniworlds
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CONCEPT
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analogy (info | search)
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WORLD
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grid_of_images_with_rule [smaller | same | bigger]
zoom in left (grid_of_analogies)
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AUTHOR
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Aaron David Fairbanks
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| BP980 |
| Bongard Problem with solution relating to concept: choice vs. Bongard Problem unrelated to this concept. |
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