The On-Line Encyclopedia of Bongard Problems

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Circled points are all possible vertices a square with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.

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	COMMENTS	`Rotation of the square is allowed.`
	CROSSREFS	`See BP1280 for version with hexagons on a hexagonal grid.` `Adjacent-numbered pages: BP1274 BP1275 BP1276 BP1277 BP1278 * BP1280 BP1281 BP1282 BP1283 BP1284`
	KEYWORD	`hard, precise, allsorted, unwordable, hardsort, left-finite, right-finite, left-full, fixedgrid, preciseworld`
	CONCEPT	`square (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1280

Circled points are all possible vertices a regular hexagon with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.

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

CROSSREFS

See BP1279 for version with squares on a square grid.

Adjacent-numbered pages: BP1275 BP1276 BP1277 BP1278 BP1279 * BP1281 BP1282 BP1283 BP1284 BP1285

KEYWORD

hard, precise, allsorted, unwordable, hardsort, left-finite, right-finite, preciseworld

AUTHOR

Leo Crabbe

BP1281

Circled points are all possible vertices an equilateral triangle with a particular side length can take, provided that each of its corners lie on a grid point vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP1276 BP1277 BP1278 BP1279 BP1280 * BP1282 BP1283 BP1284 BP1285 BP1286`
	KEYWORD	`unwordable, left-finite, right-finite, preciseworld`
	CONCEPT	`triangle (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1282

If two players take turns moving moving the black circles with the intention of capturing their opponent's piece, one can always "checkmate" the other vs. the game results in a draw if the players play optimally.

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	COMMENTS	`Players can only move their piece to a node connected to their current position. A win is secured by moving to a node your opponent is occupying.` `Which player that can force a win in left-sorted examples can change depending on who moves first.`
	CROSSREFS	`See BP1284 for an animated Problem about the same game.` `Adjacent-numbered pages: BP1277 BP1278 BP1279 BP1280 BP1281 * BP1283 BP1284 BP1285 BP1286 BP1287`
	KEYWORD	`allsorted, unwordable, notso, teach`
	CONCEPT	`capture_game (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1283

If two nodes are linked, they are each linked to a different number of nodes vs. not so.

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

	REFERENCE	`https://en.wikipedia.org/wiki/Highly_irregular_graph`
	CROSSREFS	`Adjacent-numbered pages: BP1278 BP1279 BP1280 BP1281 BP1282 * BP1284 BP1285 BP1286 BP1287 BP1288`
	CONCEPT	`graph (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1284

Both players playing "capture game" optimally vs. one or both players make mistakes.

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

	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. Optimal play can either lead to a win-lose state or a draw state.` `A frame where only one black disc is visible signifies that a player has taken the other's piece, winning the game.`
	CROSSREFS	`Adjacent-numbered pages: BP1279 BP1280 BP1281 BP1282 BP1283 * BP1285 BP1286 BP1287 BP1288 BP1289`
	KEYWORD	`teach, animated`
	CONCEPT	`capture_game (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1285

First to move wins vs. first to move loses.

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

	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`

BP1286

One frame rate vs. another.

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	COMMENTS	`In particular, 40fps vs. 20fps.`
	CROSSREFS	`Adjacent-numbered pages: BP1281 BP1282 BP1283 BP1284 BP1285 * BP1287 BP1288 BP1289 BP1290`
	KEYWORD	`stub, precise, arbitrary, antihuman, animated, contributepairs, right-couldbe, preciseworld`
	AUTHOR	`Leo Crabbe`

BP1287

Bongard Problem with solution relating to concept: chess-like capture game vs. Bongard Problem unrelated to this concept.

BP1282

BP1284

BP1285

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

	CROSSREFS	`Adjacent-numbered pages: BP1282 BP1283 BP1284 BP1285 BP1286 * BP1288 BP1289 BP1290`
	KEYWORD	`meta (see left/right), metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "capture_game"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1288

Animations vs. static images.

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

	CROSSREFS	`Adjacent-numbered pages: BP1283 BP1284 BP1285 BP1286 BP1287 * BP1289 BP1290`
	KEYWORD	`world, animated`
	AUTHOR	`Leo Crabbe`

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