Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary. And in BP2, the spectrum of values ("size") is vague, so much that the fuzzy threshold, of about half the size of the bounding box, does not seem arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary. And in BP2, the spectrum of values ("size") is vague, so much that the fuzzy threshold, of about half the size of the box, does not seem arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value. One side is the lesser side and the other is the greater side.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

The latter two typically only make sense when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

The latter two are typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

The latter two are typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." In such cases, the threshold value may be an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." This situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is never one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." The threshold value may or may not be an extreme value at the very boundary of the spectrum. For example, consider "no holes vs. one or more holes." Such a situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". It's not clear whether we should even label Bongard Problems like this as "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem also happens to be "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." The threshold value may or may not be an extreme value at the very boundary of the spectrum. For example, consider "no holes vs. one or more holes." Such a situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". It's not clear whether we should even label Bongard Problems like this as "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem is also "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." The threshold value may or may not be an extreme value at the very boundary of the spectrum. For example, consider "no holes vs. one or more holes." Such a situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". It's not clear whether we should even label Bongard Problems like this as "spectrum".

After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem is also "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." The threshold value may or may not be an extreme value at the very boundary of the spectrum. For example, consider "no holes vs. one or more holes." Such a situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". It's not clear whether we should even label Bongard Problems like this as "spectrum".

After all, any Bongard Problem can be interpreted as showing a spectrum ranging from the extreme fitting left to the extreme of fitting right.

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem is also "allsorted".

In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just a threshold value. For example, "right angles vs. obtuse angles." The threshold value may or may not be an extreme value at the very boundary of the spectrum. For example, consider "no holes vs. one or more holes." Such a situation might not even be parsed as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword "notso" left-BP867.)

Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". It's not clear whether we should even label Bongard Problems like this as "spectrum".

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete. (See BP1152.)

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?) This particular Bongard Problem is also "allsorted".

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the conditions before it are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

Many Bongard Problems are about comparison of quantity. In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

Many Bongard Problems are about comparison of quantity. In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, "acute vs. obtuse angles" does not come across as arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

Many Bongard Problems are about comparison of quantity. In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A "spectrum" Bongard Problem is usually "arbitrary" (left-BP950), since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, "acute vs. obtuse angles" does not seem arbitrary.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is "exact".

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there can be no one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

Many Bongard Problems are about comparison of quantity. In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Angles less than 90° vs. angles greater than 90°" is exact.

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is allsorted.

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is no one precise threshold number. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

Many Bongard Problems are about comparison of quantity. In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Big vs. small" is not exact.

"Angles less than 90° vs. angles greater than 90°" is exact.

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than 90° vs. angles greater than 90°" is not allsorted.

"Angles less than or equal to 90° vs. angles greater than 90°" is allsorted.

Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there is no one precise threshold number. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.

Many Bongard Problems are about comparison of quantity. In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"); to determine whether an object fits left or right, its value is then compared with a fixed threshold value. One side is lesser and the other is greater.

Spectra can be continuous or discrete.

A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of these is typically only possible to notice when the previous conditions are true.

If a spectrum Bongard Problem obeys 1) and 2), then it will be "exact" (left-BP508).

For example:

"Big vs. small" is not exact.

"Angles less than 90° vs. angles greater than 90°" is exact.

If a spectrum Bongard Problem obeys 1), 2), and 3), then it will be "allsorted" (left-BP509).

For example:

"Angles less than 90° vs. angles greater than 90°" is not allsorted.

"Angles less than or equal to 90° vs. angles greater than 90°" is allsorted.