The On-Line Encyclopedia of Bongard Problems

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BP1285

First to move wins vs. first to move loses.

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	COMMENTS	`In the depicted "capture game", the objective is to capture your opponent's piece by moving to a node they are occupying. Players take turns moving their pieces. You can only move to a node that is linked to yours. All examples are "boards" where either player can force a win, depending on who moves first.` `Players are assumed to be making optimal choices.`
	CROSSREFS	`Adjacent-numbered pages: BP1280 BP1281 BP1282 BP1283 BP1284 * BP1286 BP1287 BP1288 BP1289 BP1290`
	KEYWORD	`stub`
	CONCEPT	`capture_game (info \| search)`
	AUTHOR	`Leo Crabbe`

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.

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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`

BP1185

Smaller section tiles the grid (element-wise rotation of tiles allowed) vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1180 BP1181 BP1182 BP1183 BP1184 * BP1186 BP1187 BP1188 BP1189 BP1190`
	KEYWORD	`precise, allsorted, notso, grid, miniworlds`
	CONCEPT	`element_wise_symmetry (info \| search),` `tiling (info \| search)`
	AUTHOR	`Leo Crabbe`

BP372

Shape below fits on the left vs. shape below fits on the right.

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

	COMMENTS	`See BP805 for the version of this with box-based BPs.`
	CROSSREFS	`Adjacent-numbered pages: BP367 BP368 BP369 BP370 BP371 * BP373 BP374 BP375 BP376 BP377`
	KEYWORD	`nice, dual, handed, leftright, creativeexamples, structure, traditional, rules`
	CONCEPT	`bongard_problem (info \| search),` `categorization (info \| search),` `feature_cluster (info \| search),` `cluster (info \| search),` `choice (info \| search)`
	WORLD	`bdimage_shapes_extra_below_clear_sort [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP319

The number of dots in one cluster is a multiple of the other vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP314 BP315 BP316 BP317 BP318 * BP320 BP321 BP322 BP323 BP324`
	KEYWORD	`math, unorderedpair, traditional`
	CONCEPT	`multiple_of (info \| search),` `number (info \| search),` `dot (info \| search),` `proportional (info \| search)`
	WORLD	`two_dot_clusters [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP543

Image depicting infinitely many objects vs. image depicting finitely many objects.

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

	COMMENTS	`Another solution is "evokes infinity vs. not so." Or "seen as having arbitrarily fine detail." All left examples show objects getting smaller and smaller and closer and closer together approaching some limit within the box.`
	CROSSREFS	`Adjacent-numbered pages: BP538 BP539 BP540 BP541 BP542 * BP544 BP545 BP546 BP547 BP548`
	KEYWORD	`nice, abstract, concept, infinitedetail`
	CONCEPT	`finite_infinite (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP163

Line connecting small shapes does not intersect large one vs. line connecting small shapes intersects large one.

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

	CROSSREFS	`See BP1015 for a re-skinned version with dots instead of shapes.` `Adjacent-numbered pages: BP158 BP159 BP160 BP161 BP162 * BP164 BP165 BP166 BP167 BP168`
	KEYWORD	`traditional`
	CONCEPT	`imagined_line_or_curve (info \| search),` `imagined_entity (info \| search),` `object_line_overlap (info \| search),` `overlap (info \| search)`
	AUTHOR	`Harry E. Foundalis`

BP274

Notch from above (holds poured water) vs. no notch from above (does not hold poured water).

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

	CROSSREFS	`Adjacent-numbered pages: BP269 BP270 BP271 BP272 BP273 * BP275 BP276 BP277 BP278 BP279`
	KEYWORD	`notso, physics`
	CONCEPT	`concave_convex_region (info \| search),` `downward_upward (info \| search),` `line_absolute_direction (info \| search),` `absolute_direction (info \| search),` `direction (info \| search),` `liquid_flow (info \| search),` `gravity (info \| search)`
	WORLD	`arial_font_centered_connected_symbol [smaller \| same \| bigger]`
	AUTHOR	`Merse E. Gáspár`

BP1223

Center square is black vs. center square is white.

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

	COMMENTS	`All examples are a three by three grid of black or white squares.`
	CROSSREFS	`Adjacent-numbered pages: BP1218 BP1219 BP1220 BP1221 BP1222 * BP1224 BP1225 BP1226 BP1227 BP1228`
	KEYWORD	`stub, left-finite, right-finite, traditional, finishedexamples, fixedgrid, preciseworld`
	CONCEPT	`outlined_filled (info \| search),` `center (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP121

Objects below match their "symbols" above, according to one "code" versus objects below match their "symbols" above, according to another "code."

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

	COMMENTS	`Circle: VV; square: VΛ; triangle: ΛΛ ; blank: ΛV vs. circle: ΛΛ; square: ΛV; triangle: VV; blank: VΛ.`
	CROSSREFS	`Adjacent-numbered pages: BP116 BP117 BP118 BP119 BP120 * BP122 BP123 BP124 BP125 BP126`
	KEYWORD	`arbitrary, consistentsymbols, traditional`
	CONCEPT	`absence_as_presence (info \| search),` `correspondence (info \| search),` `sides_of_line (info \| search),` `triangle (info \| search)`
	AUTHOR	`Douglas R. Hofstadter`

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