The On-Line Encyclopedia of Bongard Problems

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Can be cut into tiles forming a checkerboard pattern vs. not so.

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	COMMENTS	`All examples in this Problem are grids consisting of two objects.`
	CROSSREFS	`Adjacent-numbered pages: BP1118 BP1119 BP1120 BP1121 BP1122 * BP1124 BP1125 BP1126 BP1127 BP1128`
	EXAMPLE	`EX9124 shows a 9 square by 9 square grid. Take each tile to be 3 squares by 3 squares; there is a 3 tile by 3 tile checkerboard pattern. (One of these tiles is itself a checkerboard pattern; the other is all black squares.)`
	KEYWORD	`hard, nice, precise, allsorted, hardsort, grid, miniworlds`
	CONCEPT	`element_grouping (info \| search)`
	AUTHOR	`Jago Collins`

BP1132

Circle that passes through points is contained within bounding box vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1127 BP1128 BP1129 BP1130 BP1131 * BP1133 BP1134 BP1135 BP1136 BP1137`
	KEYWORD	`precise, allsorted, boundingbox, hardsort, preciseworld, absoluteposition`
	CONCEPT	`circle (info \| search),` `imagined_entity (info \| search)`
	WORLD	`three_points [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1136

The removal of any one loop disentangles the whole arrangement vs. not so.

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	COMMENTS	`Left-hand examples are called "Brunnian links".`
	REFERENCE	`https://en.wikipedia.org/wiki/Brunnian_link`
	CROSSREFS	`Adjacent-numbered pages: BP1131 BP1132 BP1133 BP1134 BP1135 * BP1137 BP1138 BP1139 BP1140 BP1141`
	KEYWORD	`precise, hardsort`
	CONCEPT	`knot (info \| search)`
	WORLD	`link [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP1137

Constructible Polygon vs. Non-constructible Polygon

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	REFERENCE	`https://en.wikipedia.org/wiki/Straightedge_and_compass_construction` `https://en.wikipedia.org/wiki/Constructible_polygon`
	CROSSREFS	`Adjacent-numbered pages: BP1132 BP1133 BP1134 BP1135 BP1136 * BP1138 BP1139 BP1140 BP1141 BP1142`
	KEYWORD	`stub, precise, math, hardsort, proofsrequired, preciseworld`
	AUTHOR	`Jago Collins`

BP1245

When two players alternate coloring regions, either can force connection from top edge to bottom edge vs. either can force connection from left edge to right edge.

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	REFERENCE	`https://en.wikipedia.org/wiki/Hex_(board_game)`
	CROSSREFS	`Adjacent-numbered pages: BP1240 BP1241 BP1242 BP1243 BP1244 * BP1246 BP1247 BP1248 BP1249 BP1250`
	KEYWORD	`hard, precise, convoluted, dual, rotate, boundingbox, hardsort, challenge, proofsrequired, bordercontent`
	AUTHOR	`Aaron David Fairbanks`

BP1271

Positive correlation vs. negative correlation.

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	COMMENTS	`All examples in this Bongard Problem are scatter plots. Each dot represents a data point.` `"Positive correlation" means that when the X value increases, the Y value tends to increase as well (in the long run), while "negative correlation" means that when the X value increases, the Y value tends to decrease.`
	CROSSREFS	`Adjacent-numbered pages: BP1266 BP1267 BP1268 BP1269 BP1270 * BP1272 BP1273 BP1274 BP1275 BP1276`
	EXAMPLE	`Example TM4854 does not fit on either side because when the X value increases, the Y value stays the same.` `Example TM4855 does not fit on either side because there is no correlation.`
	KEYWORD	`fuzzy, minimal, unwordable, teach, spectrum, dual, handed, leftright, updown, rotate, stable, hardsort, left-narrow, right-narrow`
	AUTHOR	`Ben`

BP1279

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.