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BP391 There exists an edge such that removing it yields two disconnected graphs (i.e., the minimum number of edges whose removal results in two disconnected graphs is 1) vs. the minimum number of edges whose removal results in two disconnected graphs is 2.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP386 BP387 BP388 BP389 BP390  *  BP392 BP393 BP394 BP395 BP396

KEYWORD

nice, precise, traditional, preciseworld

CONCEPT graph (info | search),
distinguishing_crossing_curves (info | search),
existence (info | search),
imagined_shape (info | search),
imagined_entity (info | search)

WORLD

connected_graph [smaller | same | bigger]

AUTHOR

Jago Collins

BP392 Exponential increase vs. linear increase.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP387 BP388 BP389 BP390 BP391  *  BP393 BP394 BP395 BP396 BP397

KEYWORD

contributepairs, traditional

CONCEPT acceleration (info | search),
exponential (info | search)

AUTHOR

Jago Collins

BP393 Correct vs. incorrect.
(edit; present; nest [left/right]; search; history)
COMMENTS

"True" vs. "false."

CROSSREFS

Adjacent-numbered pages:
BP388 BP389 BP390 BP391 BP392  *  BP394 BP395 BP396 BP397 BP398

KEYWORD

nice, fuzzy, abstract, collective, contributepairs, traditional, rules, miniworlds, dithering

CONCEPT categorization (info | search),
true_false (info | search)

AUTHOR

Jago Collins

BP394 For each colored square only, there exists a path starting on it that covers each square of the figure exactly once vs. there is no path that starts on a colored square and covers each square of the figure exactly once.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP389 BP390 BP391 BP392 BP393  *  BP395 BP396 BP397 BP398 BP399

KEYWORD

hard, nice, solved, traditional, dithering, left-listable, right-listable

CONCEPT existence (info | search),
path (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Jago Collins

BP501 Easy Bongard Problems vs. hard Bongard Problems.
BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP10
BP23
BP31
BP97
BP98
BP100
BP194
BP196
BP211
BP363
BP374
BP812
BP839
BP882
BP911
BP956
BP1002
BP1015
BP1017
BP1022
BP1087
BP1095
BP1104
BP1105
BP1255
BP1260
BP112
BP162
BP344
BP383
BP394
BP559
BP564
BP793
BP795
BP796
BP801
BP825
BP831
BP842
BP849
BP860
BP871
BP872
BP875
BP876
BP877
BP878
BP898
BP899
BP927
BP934
BP944
BP954
BP965
BP998
BP1011
BP1038
BP1040
BP1055
BP1123

. . .

(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted Bongard Problems have the keyword "easy" on the OEBP.

Right-sorted Bongard Problems have the keyword "hard" on the OEBP.


"Easy" means easy for human beings to solve, not computers.

CROSSREFS

Adjacent-numbered pages:
BP496 BP497 BP498 BP499 BP500  *  BP502 BP503 BP504 BP505 BP506

KEYWORD

spectrum, subjective, meta (see left/right), links, keyword, sideless

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP503 "Nice" Bongard Problems vs. Bongard Problems the OEBP does not need more like.
BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP11
BP12
BP15
BP16
BP20
BP23
BP30
BP32
BP33
BP50
BP51
BP57
BP59
BP62
BP70
BP71
BP72
BP74
BP76
BP77
BP85
BP97
BP98
BP100
BP106
BP108

. . .

BP213
BP214
BP221
BP231
BP237
BP262
BP538
BP545
BP548
BP555
BP570
BP801
BP862
BP882
BP915
BP920
BP941
BP1000
BP1008
BP1042
BP1043
BP1129
BP1150
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted Bongard Problems have the keyword "nice" on the OEBP.

Right-sorted Bongard Problems have the keyword "less." They are not necessarily "bad," but we do not want more like them.

CROSSREFS

Adjacent-numbered pages:
BP498 BP499 BP500 BP501 BP502  *  BP504 BP505 BP506 BP507 BP508

KEYWORD

subjective, meta (see left/right), links, keyword, oebp, right-finite, left-it, feedback, time

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP504 BP pages on the OEBP in need of more examples vs. BP pages with a list of examples that should not be altered.
BP860
BP865
BP928
BP969
BP970
BP988
BP989
BP993
BP994
BP1001
BP1082
BP1085
BP1091
BP1098
BP1137
BP1206
BP1207
BP1208
BP1209
BP1210
BP1211
BP1213
BP1214
BP1215
BP1216
BP1217
BP1218
BP1220
BP1221
BP1222
BP1223
BP1224
BP1226
BP1227
BP1228

. . .

BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP10
BP11
BP12
BP13
BP14
BP15
BP16
BP17
BP18
BP19
BP20
BP21
BP22
BP23
BP24
BP25
BP26
BP27
BP28
BP29
BP30
BP32
BP33
BP34
BP35
BP36

. . .

(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted Bongard Problems have the keyword "stub" on the OEBP.

Right-sorted Bongard Problems have the keyword "finished" on the OEBP.


Users are not able to add or remove examples from Problems tagged "finished." (This is unusual; most Bongard Problems on the OEBP can be expanded indefinitely by users.)


A "finished" Bongard Problem will always admit the alternative, convoluted solution "is [left example 1] OR is [left example 2] OR . . . OR is [last left example] vs. is [right example 1] OR is [right example 2] OR . . . OR is [last right example]".

CROSSREFS

Bongard's original Problems are tagged "finished."

Adjacent-numbered pages:
BP499 BP500 BP501 BP502 BP503  *  BP505 BP506 BP507 BP508 BP509

KEYWORD

meta (see left/right), links, keyword, oebp, presentationmatters, left-finite, right-finite, instruction

WORLD

bppage [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP505 Number indicated on number line conceptually related to image shown below vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

This is the "easier version" of BP801.


All numbers on the left are canonical mathematical constants, i.e. there are no totally arbitrary ratios, with images below featuring those ratios.

CROSSREFS

Adjacent-numbered pages:
BP500 BP501 BP502 BP503 BP504  *  BP506 BP507 BP508 BP509 BP510

KEYWORD

fuzzy, math

CONCEPT number (info | search),
ratio (info | search)

AUTHOR

Aaron David Fairbanks

BP506 Bongard Problems whose solutions are hard to put into words vs. Bongard Problems whose solutions are easy to put into words.
BP159
BP524
BP956
BP964
BP981
BP998
BP1130
BP1142
BP1148
BP1149
BP1155
BP1157
BP1161
BP1181
BP1246
BP1247
BP1248
BP1250
BP1251
BP1268
BP2
(edit; present; nest [left/right]; search; history)
COMMENTS

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


"Unwordable" does not just mean convoluted, that is, involving a long description. "Unwordable" also does not just mean hard. Unwordable Bongard Problems are instead those Bongard Problems whose solutions tend to occur to people nonverbally before verbally. The typical "unwordable" Bongard Problem solution is not too difficult to see, and may be easy to describe vaguely, but hard to pin down in language.


The solution title given on the OEBP for "unwordable" pages is often something vague and evocative, further elaborated on in the comments. For example, the title for BP524 is "Same objects are shown lined up in both 'universes' vs. the two 'universes' are not aligned." If someone said this, it would be clear they had seen the answer, even though this is not a clear description.



Bongard Problems have been sorted here based on how hard they are to put into words in English. (See keyword culture.) It may be interesting to consider whether or not the same choices would be made with respect to other languages.

CROSSREFS

Adjacent-numbered pages:
BP501 BP502 BP503 BP504 BP505  *  BP507 BP508 BP509 BP510 BP511

KEYWORD

notso, subjective, meta (see left/right), links, keyword, sideless

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP507 Bongard Problems about comparison of quantity vs. other Bongard Problems.
BP2
BP11
BP12
BP28
BP29
BP34
BP36
BP37
BP38
BP53
BP62
BP65
BP67
BP79
BP173
BP176
BP196
BP211
BP292
BP338
BP501
BP565
BP869
BP882
BP915
BP971
BP972
BP978
BP1044
BP1046
BP1208
BP1
?
BP6
(edit; present; nest [left/right]; search; history)
COMMENTS

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.


A "spectrum" Bongard Problem is usually arbitrary, 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 usually be precise.

For example:

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


If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be allsorted.

For example:

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


In a discrete spectrum Bongard Problem, even if it is precise, there isn't one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)


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


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 of fitting left to the extreme of fitting right.

REFERENCE

https://en.wikipedia.org/wiki/Total_order

CROSSREFS

See BP874 for the version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP502 BP503 BP504 BP505 BP506  *  BP508 BP509 BP510 BP511 BP512

KEYWORD

notso, meta (see left/right), links, keyword, sideless

WORLD

bp [smaller | same | bigger]
zoom in left (spectrum_bp)

AUTHOR

Aaron David Fairbanks

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