Search: keyword:convoluted
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BP975 |
| Symmetric vs. Asymmetric relations between the red and blue circles. |
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COMMENTS
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Each example in this Bongard Problem consists of mini-panels containing the same arrangement of circles (ignoring colouring). Each mini-panel has a single circle highlighted in red, and possibly some circles highlighted in blue. A strict rule for this Bongard Problem could be something like "If a circle is blue in one mini-panel and red in a second mini-panel, then the red circle from the first mini-panel is blue in the second mini-panel." The relation intepretation is that a circle is related to the red circle if and only if it is coloured blue. BP973 is a similar problem. |
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CROSSREFS
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Adjacent-numbered pages:
BP970 BP971 BP972 BP973 BP974  *  BP976 BP977 BP978 BP979 BP980
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KEYWORD
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convoluted, color, infodense, rules
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AUTHOR
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Jago Collins
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BP981 |
| Each column is assigned something independently; each row is assigned something independently; there is a rule that generates contents of squares from the row information and column information vs. there is a different kind of rule. |
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COMMENTS
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To clarify the solution with an example: on the left is an image of a grid where the first row features a square with three dots and a square with nine dots, and the second row features a square with four dots and square with sixteen dots. "Three" and "four" are assigned to the rows; "x" and "x squared" are assigned to the columns.
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.
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 of this Problem.
All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey. The "rule" might be about how the images must relate to their neighbors, for example.
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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See BP979 for use of similar structures but with one square removed from the grid. Examples on the left here with any square removed should fit on the left there.
Adjacent-numbered pages:
BP976 BP977 BP978 BP979 BP980  *  BP982 BP983 BP984 BP985 BP986
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KEYWORD
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stub, convoluted, 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_operations)
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AUTHOR
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Aaron David Fairbanks
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BP990 |
| The center of mass can "see" (in straight lines) all points within the shape vs. the center of mass is not located in a region where it can see (in straight lines) all points. |
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BP1040 |
| Left is union of (non-constant) arithmetic progressions vs. not so. |
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CROSSREFS
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Adjacent-numbered pages:
BP1035 BP1036 BP1037 BP1038 BP1039  *  BP1041 BP1042 BP1043 BP1044 BP1045
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KEYWORD
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hard, precise, allsorted, convoluted, notso, handed, leftright, math, challenge, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant
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WORLD
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boxes_dots_bpimage_clear_set_of_numbers [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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