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

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

In an exact BP, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Unsorted border cases are allowed in exact BPs, but it must be clear what counts as a border case--contrast the keyword "whole" left-BP509.)

How is it determined whether or not a rule is exact? There would need to be another rule determining what the collection of examples that ought to be sorted is. A person can try to come up with increasingly thorough rules that specify what should count as a relevant example. But different ways of formalizing have slightly different consequences, and Bongard Problems by design communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to those who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

In an exact BP, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Unsorted border cases are allowed in exact BPs, but it must be clear what counts as a border case--contrast the keyword "whole" left-BP509.)

How is it determined whether or not a rule is exact? The collection of possible relevant examples is nowhere defined. A person can try to come up with increasingly thorough rules that specify what should count as a relevant example and what should not. But different ways of formalizing have slightly different consequences, and Bongard Problems by design communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

In an exact BP, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Unsorted border cases are allowed in exact BPs, but it must be clear what counts as a border case--contrast the keyword "whole" left-BP509.)

How is it determined whether or not a rule is exact? Is the collection of possible relevant examples well-defined? A person can try to come up with increasingly thorough rules that specify what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems by design communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

In an exact BP, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border case. Contrast the keyword "whole" left-BP509.)

How is it determined whether or not a rule is exact? Is the collection of possible relevant examples well-defined? A person can try to come up with increasingly thorough rules that specify what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems by design communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

In an exact BP, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border case.)

How is it determined whether or not a rule is exact? Is the collection of possible relevant examples well-defined? A person can try to come up with increasingly thorough rules that specify what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems by design communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

In an exact BP, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border case.)

What are the relevant examples for a Bongard Problem? A person can try to come up with increasingly specific rules that determine what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

A BP is exact means any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border cases.)

What are the relevant examples for a Bongard Problem? A person can try to come up with increasingly specific rules that determine what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. Whether or not such a BP should be labelled "exact" might be debated.

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

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

A BP is exact means any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border cases.)

What are the relevant examples for a Bongard Problem? A person can try to come up with increasingly specific rules that determine what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, it is unclear where some examples fit. It might be debated whether or not such BPs should be labelled exact.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

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

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

A BP is exact means any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border cases.)

What are the relevant examples for a Bongard Problem? A person can try to come up with increasingly specific rules that determine what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides take either side of an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) These BPs do seem somewhat "exact" because there is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, these BPs also seem somewhat "fuzzy": it is unclear where some examples fit.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

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

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

A BP is exact means any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted. (Border cases are allowed in exact BPs, but it must be clear what counts as a border cases.)

What are the relevant examples for a Bongard Problem? A person can try to come up with increasingly specific rules that determine what should count as a relevant example and what should not. But different ways of formalizing give slightly different results, and Bongard Problems communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise to people who see it. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides are on either side of an obvious threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) These BPs do seem somewhat "exact" because there is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, these BPs also seem somewhat "fuzzy": it is unclear where some examples fit.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

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

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

In exact Bongard Problems, it is clear where any relevant possible example should be sorted.

What are the relevant possible examples for a particular Bongard Problem? A person can try to come up with increasingly specific rules that determine what ought to count as a relevant example and what should not. Different ways of formalizing give slightly different results; Bongard Problems communicate ideas without fixing the formalization. The keyword "exact" can only mean a BP's rule seems precise. (The BP "exact vs. fuzzy" is fuzzy.)

An exact spectrum-related BP (keyword "spectrum" left-BP507) usually means the sides are on either side of an obvious threshold. For example, there is an intuitive threshold between acute and obtuse angles.

Unsorted border cases are allowed in exact BPs, but only if it is clear what the border cases are.

Sometimes the way a Bongard Problem should sort some examples is an unsolved problem in mathematics. (See e.g. BP820.) These BPs do seem somewhat "exact" because there is a clear criterion used to verify a sorted example fits where it fits--some sort of mathematical proof. However, these BPs also seem somewhat "fuzzy": it is unclear where some examples fit.

Imperfections in images should generally not be considered when deciding whether a BP is exact or fuzzy. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword "imperfectionsmatter" left-BP913.) The potential for somebody to ask whether a poorly drawn square counts as a quadrilateral does not make "triangle vs. quadrilateral" (BP6) fuzzy.

On the other hand, there are indeed many fuzzy BPs specifically about approximation (e.g. BP10: approximately triangular outline vs. approximately convex quadrilateral outline).

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 "imperfectionsmatter" (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.

Contrast "pixelperfect" (left-BP947).