Bongard Problems whose left examples alone could communicate their pattern vs. the right side is necessary to communicate what the left side is.

Bongard Problems whose left examples alone could communicate their pattern vs. other Bongard Problems.

Left-sorted BPs have the the keyword "left-narrow" on the OEBP.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other related possibilities. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is thought to be typical. If one were expecting there to be triangles, the absence of triangles would be noticeable. (See left-BP1111, the keyword "assuming", for Bongard Problems that require the solver to go in with special expectations.)

And a person might notice the absence of triangles in a collection of just polygons because a triangle is such a typical example of a polygon. On the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Both sides of a BP can be narrow, e.g. BP6.

Further, a pattern and its direct negation can be narrow, e.g. BP20.

Note that this is not just BP514 ("right-narrow") flipped.

Bongard Problems whose left examples alone could communicate the pattern vs. other Bongard Problems.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other related possibilities. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is thought to be typical. If one were expecting there to be triangles, the absence of triangles would be noticeable. (See left-BP1111, the keyword "assuming", for Bongard Problems that require the solver to go in with special expectations.)

And a person might notice the absence of triangles in a collection of just polygons because a triangle is such a typical example of a polygon. On the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Both sides of a BP can be narrow, e.g. BP6.

Further, a pattern and its direct negation can be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other related possibilities. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is thought to be typical. If one were expecting there to be triangles, the absence of triangles would be noticeable. (See left-BP1111, the keyword "assuming", for Bongard Problems that require the solver to go in with special expectations.)

A person might notice the absence of triangles in a collection of polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Both sides of a BP can be narrow, e.g. BP6.

Further, a pattern and its direct negation can be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Both sides of a BP can be narrow, e.g. BP6.

Further, a pattern and its direct negation can be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Both sides of a BP can be narrow, e.g. BP6.

More specifically, a pattern and its direct negation can be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Both sides of a BP can be narrow, e.g. BP6.

More specifically, a pattern and its negation can be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow pattern. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a BP to be narrow, e.g. BP6.

More specifically, it is possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a BP to be narrow, e.g. BP6.

More specifically, it is possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow pattern seems smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of other polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a BP to be narrow, e.g. BP6.

More specifically, it is possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

A narrow pattern seems intuitively smaller in comparison to the space of other possible related examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of other polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a BP to be narrow, e.g. BP6.

More specifically, it is possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

A narrow pattern of examples seems intuitively smaller in comparison to the space of possible examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of other polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a BP to be narrow, e.g. BP6.

More specifically, it is possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

A narrow pattern of examples seems intuitively smaller in comparison to the space of possible examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly thought to be typical. A person might notice the absence of triangles in a collection of other polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a problem to be narrow, e.g. BP6.

It is furthermore possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

A narrow pattern of examples seems intuitively smaller in comparison to the space of possible examples. Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what is implicitly seen as typical. A person might notice the absence of triangles in a collection of other polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

It is possible for both sides of a problem to be narrow, e.g. BP6.

It is furthermore possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.

Call a pattern "narrow" if it is likely to be noticed in a huge collection of examples, without any counterexamples provided.

A huge collection of triangles will be recognized as such; "triangles" is a narrow pattern. A huge collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

A narrow pattern of examples seems intuitively smaller in comparison to all possible examples (even despite if both are infinite). Narrow patterns tend to be phrased positively ("is [property]"), while non-narrow patterns opposite narrow patterns tend to be phrased negatively ("is not [property]").

It makes a difference what sort of examples are implicitly seen as typical. A person might notice the absence of triangles in a collection of other polygons because a triangle is such a typical example of a polygon; on the other hand, a person will probably not notice the absence of 174-gons.

It is possible for both sides of a problem to be narrow, e.g. BP6.

It is furthermore possible for a pattern and its negation to be narrow, e.g. BP20.

Note that this is not just BP514 flipped.