The On-Line Encyclopedia of Bongard Problems

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BP230

The sum of vertices, line ends, and dots is 7 vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP225 BP226 BP227 BP228 BP229 * BP231 BP232 BP233 BP234 BP235`
	KEYWORD	`arbitrary, traditional`
	CONCEPT	`addition (info \| search),` `line_or_curve_endpoint (info \| search),` `dot (info \| search),` `vertex_of_meeting_lines (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP987

Solution could appear in a Bongard Problem featuring an image of itself on either of its sides vs. solution can appear in a Bongard Problem featuring an image of itself on a certain side only.

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	COMMENTS	`All examples are Bongard Problems fitting left in BP954.` `This is very close to BP927, specialized to Bongard Problems fitting left in BP954. The difference is that a Bongard Problem solution would fit left in BP927 but right here if it can sort images of it on both sides, but it is impossible to make an image of it fractally including itself on a certain side. An example is EX7997.` `Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit right here.`
	CROSSREFS	`Adjacent-numbered pages: BP982 BP983 BP984 BP985 BP986 * BP988 BP989 BP990 BP991 BP992`
	KEYWORD	`abstract, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant, visualimagination`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP897

Wide angles connected to narrow angles vs. not so.

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	COMMENTS	`Another solution is that right examples can be folded down flat onto one isosceles triangle while left examples cannot.` `All examples in this Problem feature four isosceles triangles connected by corners and/or edges.`
	CROSSREFS	`This was conceived as a false solution for BP898.` `Adjacent-numbered pages: BP892 BP893 BP894 BP895 BP896 * BP898 BP899 BP900 BP901 BP902`
	KEYWORD	`precise, allsorted, notso, traditional, preciseworld`
	CONCEPT	`triangle (info \| search)`
	WORLD	`[smaller \| same \| bigger]`
	AUTHOR	`Molly C Klenzak, Aaron David Fairbanks`

BP155

Curves are longer than straight lines vs. curves are shorter than straight lines.

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	CROSSREFS	`Adjacent-numbered pages: BP150 BP151 BP152 BP153 BP154 * BP156 BP157 BP158 BP159 BP160`
	KEYWORD	`traditional`
	CONCEPT	`curved_straight (info \| search),` `length_line_or_curve (info \| search),` `specific_style (info \| search),` `specificity (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP229

When the objects are rotated and their dots are overlapped and eliminated, they form three-square-tall structures with columns of the same color vs. not so.

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	COMMENTS	`Explanation / justification of BP229 by its creator:` `"Long (doubly sized) objects are purines (A & G).` `Short objects are pyrimidines (C & T).` `Black are those forming triple Hbond (G and C).` `White are those forming double Hbond (A & T).` `On the left we have matching codes, i.e., bases, doublets or triplets that, when rotated, can pair correctly (A with T, G with C), binding the two strands.` `On the right we have objects that no matter how they are rotated they do not pair correctly (because of bumps, wrong color codes, etc)."`
	CROSSREFS	`Adjacent-numbered pages: BP224 BP225 BP226 BP227 BP228 * BP230 BP231 BP232 BP233 BP234`
	KEYWORD	`unorderedpair, traditional`
	CONCEPT	`rotation_required (info \| search),` `tiling (info \| search),` `specific_value (info \| search),` `specificity (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP296

All three sizes are present vs. only two of the three sizes present.

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	CROSSREFS	`Adjacent-numbered pages: BP291 BP292 BP293 BP294 BP295 * BP297 BP298 BP299 BP300 BP301`
	KEYWORD	`traditional`
	CONCEPT	`all (info \| search),` `existence (info \| search),` `number (info \| search)`
	AUTHOR	`"Lewis"`

BP91

Three identical elements vs. four identical elements.

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	REFERENCE	`M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 244.`
	CROSSREFS	`BP1226 is "three identical elements vs. other number of identical elements".` `Adjacent-numbered pages: BP86 BP87 BP88 BP89 BP90 * BP92 BP93 BP94 BP95 BP96`
	KEYWORD	`number, ignoreimperfections, finished, traditional, bongard`
	CONCEPT	`indentation (info \| search),` `on_line_or_curve (info \| search),` `number (info \| search),` `protrusion (info \| search),` `separation_of_joined_objects (info \| search),` `same (info \| search),` `three (info \| search),` `four (info \| search)`
	WORLD	`curves_and_fill_shapes_drawing [smaller \| same \| bigger]`
	AUTHOR	`Mikhail M. Bongard`

BP945

Cube number of dots vs. non-cube number of dots.

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	CROSSREFS	`Adjacent-numbered pages: BP940 BP941 BP942 BP943 BP944 * BP946 BP947 BP948 BP949 BP950`
	KEYWORD	`precise, allsorted, number, left-null, help, preciseworld`
	CONCEPT	`cube (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP103

Isosceles triangle vs. scalene triangle.

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	CROSSREFS	`Adjacent-numbered pages: BP98 BP99 BP100 BP101 BP102 * BP104 BP105 BP106 BP107 BP108`
	KEYWORD	`precise, allsorted, stretch, orderedpair, traditional, preciseworld`
	CONCEPT	`line_or_curve_endpoint (info \| search),` `length_line_or_curve (info \| search),` `imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `same_feature (info \| search),` `same (info \| search),` `isosceles_triangle (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP293

Square divided into four areas of the same size and shape vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP288 BP289 BP290 BP291 BP292 * BP294 BP295 BP296 BP297 BP298`
	KEYWORD	`nice, traditional`
	CONCEPT	`square (info \| search),` `same_shape (info \| search),` `same (info \| search)`
	AUTHOR	`"Lewis"`

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