The On-Line Encyclopedia of Bongard Problems

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BP150

Odd number of squares vs. even number of squares.

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

	CROSSREFS	`Adjacent-numbered pages: BP145 BP146 BP147 BP148 BP149 * BP151 BP152 BP153 BP154 BP155`
	KEYWORD	`number, traditional`
	CONCEPT	`even_odd (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

BP202

Even number vs. odd number.

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

	CROSSREFS	`See BP334 for a version of the same idea, but using dots instead of arbitrary shapes.` `Adjacent-numbered pages: BP197 BP198 BP199 BP200 BP201 * BP203 BP204 BP205 BP206 BP207`
	KEYWORD	`noisy, number, traditional`
	CONCEPT	`even_odd (info \| search)`
	AUTHOR	`Giuseppe Insana`

BP267

Odd number of straight line segments vs. even number of straight line segments.

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

	CROSSREFS	`Adjacent-numbered pages: BP262 BP263 BP264 BP265 BP266 * BP268 BP269 BP270 BP271 BP272`
	CONCEPT	`even_odd (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP334

Odd number of dots vs. even number of dots.

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

	CROSSREFS	`See BP334 for a version of the same idea, but using arbitrary shapes instead of dots.` `Adjacent-numbered pages: BP329 BP330 BP331 BP332 BP333 * BP335 BP336 BP337 BP338 BP339`
	KEYWORD	`precise, allsorted, number, math, left-narrow, right-narrow, right-null, help, traditional, preciseworld`
	CONCEPT	`even_odd (info \| search)`
	WORLD	`dots [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP560

There exists a closed trail that hits each edge exactly once vs. not so.

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

	COMMENTS	`Left examples are called "Eulerian graphs."` `A connected graph is Eulerian if and only if each vertex is incident to an even number of edges.`
	CROSSREFS	`Adjacent-numbered pages: BP555 BP556 BP557 BP558 BP559 * BP561 BP562 BP563 BP564 BP565`
	KEYWORD	`precise, allsorted, math, traditional, preciseworld`
	CONCEPT	`graph (info \| search),` `distinguishing_crossing_curves (info \| search),` `all (info \| search),` `even_odd (info \| search),` `existence (info \| search)`
	WORLD	`connected_graph [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP889

Odd number of enclosed regions vs. even number of enclosed regions.

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

	COMMENTS	`The use of numbers and pictures are only a distraction.` `See BP966 for the version in which the background counts.`
	CROSSREFS	`Adjacent-numbered pages: BP884 BP885 BP886 BP887 BP888 * BP890 BP891 BP892 BP893 BP894`
	KEYWORD	`number`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Thomas Joyce`

BP922

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.

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

	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`

BP966

Even number of white regions vs. odd number of white regions.

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

	COMMENTS	`See BP889 for the version in which the background doesn't count.`
	CROSSREFS	`Adjacent-numbered pages: BP961 BP962 BP963 BP964 BP965 * BP967 BP968 BP969 BP970 BP971`
	KEYWORD	`nice, boundingbox, number, right-null, perfect, pixelperfect, traditional, bordercontent`
	CONCEPT	`separated_regions (info \| search),` `even_odd (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1150

Even BP number on the OEBP vs. odd BP number on the OEBP.

	BP2	BP4	BP6	BP8	BP10	BP12
	BP14	BP16	BP18	BP20	BP100	BP1150

	BP1	BP3	BP5	BP7	BP9	BP11
	BP13	BP15	BP17	BP19	BP1073

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

	COMMENTS	`This was created as an example for BP1073 (left-it versus right-it).`
	CROSSREFS	`Adjacent-numbered pages: BP1145 BP1146 BP1147 BP1148 BP1149 * BP1151 BP1152 BP1153 BP1154 BP1155`
	KEYWORD	`less, meta (see left/right), links, oebp, example, left-self, presentationmatters, right-it, experimental, left-listable, right-listable`
	CONCEPT	`even_odd (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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