The On-Line Encyclopedia of Bongard Problems

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BP279

The left part has more pixels (area) than the right part vs. the left part has fewer pixels than the right part.

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	CROSSREFS	`Adjacent-numbered pages: BP274 BP275 BP276 BP277 BP278 * BP280 BP281 BP282 BP283 BP284`
	KEYWORD	`dual, handed, leftright, pixelperfect`
	CONCEPT	`left_right (info \| search),` `length_line_or_curve (info \| search),` `area (info \| search)`
	WORLD	`arial_font_two_symbols [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP221

No small square at the end of any curve vs. curve ends at a small square.

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	CROSSREFS	`Adjacent-numbered pages: BP216 BP217 BP218 BP219 BP220 * BP222 BP223 BP224 BP225 BP226`
	KEYWORD	`less, traditional`
	CONCEPT	`existence (info \| search),` `curve_texture (info \| search),` `texture (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP324

Left shapes can be placed on top of each other to make right shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP319 BP320 BP321 BP322 BP323 * BP325 BP326 BP327 BP328 BP329`
	KEYWORD	`precise, unstable, perfect, pixelperfect, structure, orderedtriplet, traditional`
	CONCEPT	`set_union (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1017

Line segments linking same-coloured dots would intersect vs. not so.

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	CROSSREFS	`This is a less noisy version of BP261.` `Adjacent-numbered pages: BP1012 BP1013 BP1014 BP1015 BP1016 * BP1018 BP1019 BP1020 BP1021 BP1022`
	KEYWORD	`easy, nice, precise, allsorted, perfect, traditional, finishedexamples, preciseworld`
	CONCEPT	`lines_coincide (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `overlap (info \| search)`
	AUTHOR	`Leo Crabbe`

BP166

Two clusters vs. three clusters.

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	CROSSREFS	`Adjacent-numbered pages: BP161 BP162 BP163 BP164 BP165 * BP167 BP168 BP169 BP170 BP171`
	KEYWORD	`traditional`
	CONCEPT	`number (info \| search),` `dot (info \| search),` `feature_cluster (info \| search),` `cluster_of_one (info \| search),` `cluster (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`Multiple options: dot_clusters [smaller \| same \| bigger], point_clusters [smaller \| same \| bigger]`
	AUTHOR	`Harry E. Foundalis`

BP1068

Every nonempty region has two boxes vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1063 BP1064 BP1065 BP1066 BP1067 * BP1069 BP1070 BP1071 BP1072 BP1073`
	KEYWORD	`arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `two (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP303

Three objects are identical, the fourth differs vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP298 BP299 BP300 BP301 BP302 * BP304 BP305 BP306 BP307 BP308`
	KEYWORD	`noisy, traditional, fixedgrid`
	CONCEPT	`same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

BP145

Different ways of grouping yield same 4-1 split vs. different ways of grouping yield different 4-1 splits.

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	CROSSREFS	`Adjacent-numbered pages: BP140 BP141 BP142 BP143 BP144 * BP146 BP147 BP148 BP149 BP150`
	KEYWORD	`traditional, miniworlds`
	CONCEPT	`and (info \| search),` `number (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `same_shape (info \| search),` `same (info \| search),` `similar_shape (info \| search),` `similar (info \| search),` `one (info \| search),` `four (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP1015

Segment drawn between two points intersects another line vs segment drawn between two points does not intersect any other lines

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	CROSSREFS	`This is nearly identical to BP163. Here instead of shape outlines dots are used, and the dots can be within the larger shape outline.` `Adjacent-numbered pages: BP1010 BP1011 BP1012 BP1013 BP1014 * BP1016 BP1017 BP1018 BP1019 BP1020`
	KEYWORD	`easy, precise`
	CONCEPT	`dot (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `object_line_overlap (info \| search),` `overlap (info \| search)`
	AUTHOR	`Peter Nesin`

BP1125

BP pages on the OEBP (with a criterion for sorting examples that in some cases may be very difficult to work out) where users should be certain (i.e. know a proof) about how examples are sorted vs. users can include examples on a side as long as nobody has seen a reason it does not fit there.

	BP335	BP344	BP532	BP850	BP1119	BP1137
	BP1200	BP1245

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	COMMENTS	`Left-sorted Bongard Problems have the keyword "proofsrequired" on the OEBP.` `Right-sorted Bongard Problems have the keyword "noproofs" on the OEBP.` `For every "noproofs" Bongard Problem there could be made a stricter "proofsrequired" version. This stricter version will be hardsort.` `Deciding to make a Bongard Problem noproofs adds subjectivity to the sorting of examples (keyword subjective).` `One interpretation of topology (a subject of mathematics -- see https://en.wikipedia.org/wiki/Topology ) is that a topology describes the observability of various properties. (The topological "neighborhoods" of a point are the subsets one could determine the point to be within using a finite number of measurements.) The analogue of restricting to just the cases where a property is observably true (i.e. "proofsrequired") corresponds to taking the topological "interior" of that property.` `TO DO: It may be better to split each of these keywords up into two: "left-proofsrequired", "right-proofsrequired", "left-noproofs", "right noproofs".`
	CROSSREFS	`See keyword hardsort.` `Bongard Problems that are left-unknowable or right-unknowable will have to be "noproofs".` `Adjacent-numbered pages: BP1120 BP1121 BP1122 BP1123 BP1124 * BP1126 BP1127 BP1128 BP1129 BP1130`
	EXAMPLE	`In "proofsrequired" BP335 (shape tessellates the plane vs. shape does not tessellate the plane), shapes are only put in the Bongard Problem if they are known to tessellate or not to tessellate the plane. A "noproofs" version of this Bongard Problem would instead allow a shape to be put on the right if it was just (subjectively) really hard to find a way of tessellating the plane with it.`
	KEYWORD	`meta (see left/right), links, keyword, oebp, instruction`
	AUTHOR	`Aaron David Fairbanks`

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