The On-Line Encyclopedia of Bongard Problems

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One row is rearranged to make the other by swapping an odd number of object pairs vs. one row is rearranged to make the other by swapping an even number of object pairs.

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	COMMENTS	`The mathematical terms for these operations are even and odd permutations.`
	CROSSREFS	`Adjacent-numbered pages: BP917 BP918 BP919 BP920 BP921 * BP923 BP924 BP925 BP926 BP927`
	KEYWORD	`precise, allsorted, math, left-narrow, right-narrow, unorderedpair, preciseworld, left-listable`
	CONCEPT	`even_odd (info \| search),` `permutation (info \| search)`
	AUTHOR	`Leo Crabbe`

BP924

Polygons where all sides are different lengths vs. Polygons where not all sides are different lengths.

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	COMMENTS	`All examples in this Problem are outlines of convex polygons.` `This is a generalisation of scalene triangles to any polygon.`
	CROSSREFS	`The left side implies the right side of BP329 (regular vs. irregular polygons), but the converse is not true.` `The left side of BP329 implies the right side, but the converse is not true.` `Adjacent-numbered pages: BP919 BP920 BP921 BP922 BP923 * BP925 BP926 BP927 BP928 BP929`
	EXAMPLE	`Any scalene triangle will fit on the left, because no two sides are equal.` `However, any regular polygon will not fit on the left, because all of its sides are equal.` `A random convex polygon will "almost surely" fit on the left.`
	KEYWORD	`nice, stretch, right-narrow, traditional`
	CONCEPT	`all (info \| search)`
	WORLD	`polygon_outline [smaller \| same \| bigger]`
	AUTHOR	`Jago Collins`

BP932

Every vertex is connected to every other vs. vertices are connected in a cycle (no other connections).

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	COMMENTS	`Complete graphs with zero, one, two, or three vertices would be ambiguously categorized (fit in overlap of both sides).` `Left examples are called "fully connected graphs." Right examples are called "cycle graphs."`
	CROSSREFS	`Adjacent-numbered pages: BP927 BP928 BP929 BP930 BP931 * BP933 BP934 BP935 BP936 BP937`
	KEYWORD	`precise, left-narrow, right-narrow, both, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `loop (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1049

3 in a row vs. not

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

	CROSSREFS	`Adjacent-numbered pages: BP1044 BP1045 BP1046 BP1047 BP1048 * BP1050 BP1051 BP1052 BP1053 BP1054`
	KEYWORD	`teach, creativeexamples, left-narrow, right-narrow, contributepairs, fixedgrid, miniworlds`
	CONCEPT	`three (info \| search)`
	AUTHOR	`Jago Collins`

BP1171

Visual Bongard Problems where switching black and white in any sorted example renders the example unsortable vs. visual Bongard Problems where some example can have its colours inverted and remain sorted.

BP5

BP962

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	COMMENTS	`Most visual BPs will be sorted left by this problem, as examples usually have white backgrounds by default.`
	CROSSREFS	`Adjacent-numbered pages: BP1166 BP1167 BP1168 BP1169 BP1170 * BP1172 BP1173 BP1174 BP1175 BP1176`
	KEYWORD	`meta (see left/right), links, sideless, right-narrow, problemkiller`
	AUTHOR	`Leo Crabbe`

BP1213

Axis of symmetry along the NW/SE diagonal vs. axis of symmetry along the NE/SW diagonal

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	CROSSREFS	`Adjacent-numbered pages: BP1208 BP1209 BP1210 BP1211 BP1212 * BP1214 BP1215 BP1216 BP1217 BP1218`
	KEYWORD	`stub, dual, handed, leftright, updown, rotate, stretch, left-narrow, right-narrow, traditional, both`
	CONCEPT	`diagonal (info \| search),` `symmetry_axis (info \| search),` `symmetry (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1216

Arrow pointing north-west vs. arrow pointing south-east.

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	CROSSREFS	`BP1218 is "arrow pointing north-west vs. arrow pointing elsewhere".` `Adjacent-numbered pages: BP1211 BP1212 BP1213 BP1214 BP1215 * BP1217 BP1218 BP1219 BP1220 BP1221`
	KEYWORD	`stub, precise, dual, handed, leftright, updown, rotate, left-narrow, right-narrow, traditional`
	CONCEPT	`diagonal (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1219

Blank image (square) vs. image of blank square.

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	CROSSREFS	`See also BP1056, "blank image vs. nothing".` `BP1 is also a (less specific) solution to this.` `BP1209 (flipped) is also a (less specific) solution to this.` `Adjacent-numbered pages: BP1214 BP1215 BP1216 BP1217 BP1218 * BP1220 BP1221 BP1222 BP1223 BP1224`
	KEYWORD	`minimal, gap, left-narrow, right-narrow, left-finite, right-finite, left-full, right-full, left-null, funny, unstableworld`
	CONCEPT	`empty (info \| search),` `square (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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