Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. There is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximates triangle vs. closely approximates quadrilateral." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes there would be a spectrum of how closely a shape approximates something; clearly there are ambiguously ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. There is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximates triangle vs. closely approximates quadrilateral." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes there would be a spectrum of how closely a shape approximates something; there are ambiguously ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. There is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximates triangle vs. closely approximates quadrilateral." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes there would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximates triangle vs. closely approximates quadrilateral." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes there would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximates triangle vs. closely approximates quadrilateral." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximates triangle vs. closely approximates quadrilateral." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangles vs. quadrilateral" (BP6) non-exact; a shape in the abstract is either a quadrilateral or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximate triangles vs. closely approximate quadrilaterals." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and quadrilaterals, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a square does not make "triangles vs. squares" (BP6) non-exact; a shape in the abstract is either a square or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect renderings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximate triangles vs. closely approximate squares." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and squares, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for somebody to ask whether a poorly drawn square counts as a square does not make "triangles vs. squares" (BP6) non-exact; a shape in the abstract is either a square or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect drawings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximate triangles vs. closely approximate squares." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and squares, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the potential for a poorly drawn square does not make "triangles vs. squares" (BP6) non-exact; a shape in the abstract is either a square or it isn't. In general, on the OEBP we imagine that a geometry-based solution is about ideal shapes with smooth edges, straight lines, crisp corners, etc., while the included images of examples on the page are imperfect drawings of those shapes. Clearly there is room for ambiguity here, because, given only the images included for BP6, it is possible to parse the solution as "closely approximate triangles vs. closely approximate squares." However, that is not the solution we have listed on the page BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and squares, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (left-BP913). Otherwise, when deciding whether a Problem idea is "exact" or not, imagine all the examples were drawn perfectly. For example, the case of a "poorly drawn square" does not make "triangles vs. squares" (BP6) non-exact; a shape in the abstract is either a square or it isn't. In general, on the OEBP we imagine that a geometry-based solution is actually about ideal shapes with smooth edges, straight lines, crisp corners, etc., and the included images of examples are imperfect drawings of them. Clearly there is room for ambiguity here, because, given the images included for BP6, it is possible to parse the solution as "closely approximate triangles vs. closely approximate squares." However, that is not the solution we have listed on the page for BP6; we have instead decided to make that page on the encyclopedia be about the abstract ideas of triangles and squares, without cluttering it up by involving irrelevant ideas about close approximation.

For Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even with ideal perfectly drawn shapes would be a spectrum of how closely a shape approximates something; there are ambiguous cases here, so the Problem is not exact.

Left examples have the keyword "exact" on the OEBP.

Right examples have the keyword "fuzzy" on the OEBP.

In exact Bongard Problems, it is always clear where each relevant example should be sorted. Ambiguity is allowed, but only if it is clear precisely which cases are ambiguous.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

IMPORTANT: For Bongard Problems based on images we assume the intended geometry represented by the image is understood before we sort. The case of a "poorly drawn square" is not here considered an ambiguous case for BP6 triangles vs. squares; a shape is either a square or it isn't.

However, for Bongard Problems specifically about approximation (e.g. BP10 approximately triangular outline vs. approximately convex quadrilateral outline) even in the pure geometry there is a spectrum of how closely a shape approximates something; there are ambiguous cases here.

For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "literalgeometry" (BP913).