LouisJalouzot/oebp · Datasets at Hugging Face

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1	Empty image vs. non-empty image.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.	The first Bongard Problem. All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).	A circle fits on the right because it is not nothing.		Mikhail M. Bongard	2023-06-18 19:55:03	1967-01-01 00:00:00	[ "easy", "nice", "finished", "precise", "allsorted", "left-narrow", "left-finite", "world", "traditional", "left-null", "left-full", "bongard", "perfect", "pixelperfect", "unstable", "stableworld", "deformstable" ]	[ "empty", "nothing", "existence", "zero", "0" ]
2	Big vs. small.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.	The meaning of "big" left intentionally vague. There are various specific ways to define size, such as diameter, minimum distance between points on edge, and size of smallest bounding circle. All examples in this Bongard Problem are single simple shapes, either outlines or solid black. All examples on the same side a...			Mikhail M. Bongard	2024-09-19 05:50:19	1967-01-01 00:00:00	[ "easy", "nice", "finished", "spectrum", "fuzzy", "traditional", "size", "bongard", "stable", "continuous" ]	[ "size", "large", "small", "big" ]
3	Hollow outline vs. filled in solid.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.	All examples in this Bongard Problem are single simple shapes.			Mikhail M. Bongard	2023-06-16 20:43:59	1967-01-01 00:00:00	[ "easy", "nice", "finished", "precise", "allsorted", "world", "traditional", "bongard", "gap", "preciseworld" ]	[ "outlined_filled", "color", "filled", "texture" ]
4	Convex vs. concave.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.	All examples in this Problem are outlines of shapes or solid black shapes.		BP136 is the same solution (flipped) but with only polygonal outlines and also with extraneous dots distracting from the solution.	Mikhail M. Bongard	2023-06-16 20:06:35	1967-01-01 00:00:00	[ "easy", "nice", "finished", "precise", "right-narrow", "traditional", "bongard", "unstable" ]	[ "concave_convex_angle" ]
5	Is polygon vs. is smooth without straight lines or corners.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.	All examples in this Bongard Problem are outlines of shapes.			Mikhail M. Bongard	2022-12-28 15:44:45	1967-01-01 00:00:00	[ "easy", "nice", "finished", "traditional", "bongard", "ignoreimperfections" ]	[ "curved_straight" ]
6	Triangle vs. quadrilateral.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.	All examples in this Problem are outlines of polygons or solid black polygons.		BP1211 is "triangle vs. anything else".	Mikhail M. Bongard	2023-06-16 16:24:36	1967-01-01 00:00:00	[ "easy", "nice", "finished", "precise", "traditional", "number", "bongard", "ignoreimperfections", "preciseworld" ]	[ "number", "triangle", "three", "3", "four", "4" ]
7	Taller than wide vs. wider than tall.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.	All examples in this Bongard Problem are oblong connected figures made up of some curves. Shapes as tall as they are wide would be ambiguous.			Mikhail M. Bongard	2022-12-27 11:17:09	1967-01-01 00:00:00	[ "easy", "nice", "finished", "dual", "traditional", "handed", "rotate", "bongard", "stretch" ]	[ "horizontal", "line_slope", "vertical", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
8	Positioned right vs. positioned left.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.	Center of shape's x coordinate is higher than zero (where zero is the middle of the picture). All examples in this Bongard Problem are small shape outlines. This is the first Bongard Problem in which absolute positioning is relevant. Shapes close to the middle would be ambiguous.			Mikhail M. Bongard	2022-12-27 11:17:40	1967-01-01 00:00:00	[ "easy", "nice", "finished", "dual", "leftright", "traditional", "handed", "bongard", "boundingbox", "absoluteposition" ]	[ "absolute_position", "bounding_box", "coordinate", "left_right" ]
9	Non-wiggly outline vs. wiggly outline.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.	"Wiggly" means a high number of small concavities adjacent to one another all around the outline. All examples in this Bongard Problem are shape outlines. Shapes with outlines that are only wiggly within partial sections would be ambiguous. Shapes with outlines that have many medium-size concavities would be ambiguou...			Mikhail M. Bongard	2023-06-15 08:54:23	1967-01-01 00:00:00	[ "easy", "nice", "finished", "fuzzy", "world", "traditional", "bongard", "stable" ]	[ "curve_texture", "texture" ]
10	Approximately triangular outline vs. approximately convex quadrilateral outline.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.	All examples in this Bongard Problem are shape outlines.			Mikhail M. Bongard	2023-06-16 21:35:47	1967-01-01 00:00:00	[ "easy", "finished", "fuzzy", "noisy", "traditional", "number", "bongard" ]	[ "number", "three", "3", "four", "4" ]
11	Thin and elongated vs. compact.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.	All examples in this Bongard Problem are shape outlines.			Mikhail M. Bongard	2023-01-05 22:01:57	1967-01-01 00:00:00	[ "nice", "finished", "spectrum", "fuzzy", "world", "traditional", "bongard", "stable", "stretch" ]	[ "elongated_compact" ]
12	Thin elongated convex hull vs. compact convex hull.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.	All examples in this Bongard Problem are shape outlines.			Mikhail M. Bongard	2022-12-27 11:38:24	1967-01-01 00:00:00	[ "nice", "finished", "spectrum", "fuzzy", "traditional", "bongard", "stretch" ]	[ "convex_hull", "elongated_compact" ]
13	Tall rectangle OR wide ellipse vs. wide rectangle OR tall ellipse.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.	All examples in this Bongard Problem are outlines of ellipses or rectangles aligned to the x-y-axes.			Mikhail M. Bongard	2023-01-05 22:01:27	1967-01-01 00:00:00	[ "finished", "precise", "traditional", "bongard", "stretch", "preciseworld" ]	[ "or", "disjunction logical", "horizontal", "line_slope", "vertical" ]
14	All big individual figures vs. all small individual figures.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.	All examples in this Problem show one or more connected figures made up of lines. Some big shapes and some small shapes would be ambiguous.		See BP2 for the same idea using one shape.	Mikhail M. Bongard	2023-01-05 22:02:18	1967-01-01 00:00:00	[ "finished", "fuzzy", "traditional", "size", "bongard", "stable" ]	[ "all", "length_line_or_curve", "size", "large", "small", "big" ]
15	Closed shape outline vs. non-closed curve.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.	All examples in this Bongard Problem are non-self-intersecting curves.			Mikhail M. Bongard	2023-06-25 13:32:03	1967-01-01 00:00:00	[ "nice", "finished", "world", "traditional", "bongard", "unstable" ]	[ "closed_open", "hole", "loop" ]
16	Clockwise spiraling curve vs. counter-clockwise spiraling curve.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.	All examples in this Bongard Problem are non-self-intersecting spiraling curves, perhaps wiggly, perhaps with corners.			Mikhail M. Bongard	2023-06-16 16:44:57	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "handed", "bongard", "gap" ]	[ "turn_orientation", "tracing_line_or_curve", "rotational_direction", "direction" ]
17	Shape with a reflex corner vs. shape without a reflex corner.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.	All examples in this Bongard Problem are outlines of shapes.			Mikhail M. Bongard	2022-12-27 11:40:26	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "acute", "angle", "indentation", "notch" ]
18	"Pinched" shape (drastically thinner somewhere in the middle than on the ends) vs. non-pinched shape.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.	All examples in this Bongard Problem are oblong outlines of shapes.			Mikhail M. Bongard	2022-12-27 11:39:38	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "neck_narrowing" ]
19	Horizontal pinch vs. vertical pinch.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.	All examples in this Bongard Problem are outlines of shapes. More specifically, all examples have a thin horizontal or vertical bridge in the middle connecting two wide ends.			Mikhail M. Bongard	2022-12-27 11:38:43	1967-01-01 00:00:00	[ "finished", "dual", "traditional", "rotate", "bongard" ]	[ "horizontal", "neck_narrowing", "vertical" ]
20	Both dots touching same bulb vs. dots on opposite bulbs.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.	All examples in this Bongard Problem are outlines of smooth shapes with a pinch in the middle and with two tiny black circles attached to the outside of the shape (tangent). A shape with either dot tangent to the the valley section would be ambiguous.			Mikhail M. Bongard	2022-12-27 11:36:17	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard" ]	[ "near_far", "close to", "far from", "together", "neck_narrowing", "separation_of_joined_objects" ]
21	Small shape present vs. all shapes large.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.	All examples in this problem include three or fewer outlines of circles and (non-skinny) triangles.			Mikhail M. Bongard	2022-12-27 11:40:27	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "existence", "size", "large", "small", "big" ]
22	All shapes approximately the same size vs. shapes of different size.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.	All examples in this problem include three or fewer outlines of circles, (near-square) quadrilaterals and (non-skinny) triangles.			Mikhail M. Bongard	2022-12-27 11:39:38	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "all", "average", "size", "large", "small", "big" ]
23	One vs. two figures.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.	All examples in this Problem comprise one or two shape outlines.			Mikhail M. Bongard	2022-12-28 16:29:06	1967-01-01 00:00:00	[ "easy", "nice", "finished", "precise", "world", "traditional", "number", "bongard", "gap" ]	[ "number", "one", "1", "two", "2" ]
24	A circle vs. no circle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.	All small squares appearing in this problem are axis-aligned.			Mikhail M. Bongard	2023-06-16 16:28:00	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "circle", "existence" ]
25	Black figure is a triangle vs. black figure is a circle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.	All small squares appearing in this problem are axis-aligned.			Mikhail M. Bongard	2022-12-27 11:40:27	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture", "triangle" ]
26	Solid black triangle vs. no solid black triangle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.				Mikhail M. Bongard	2022-12-27 11:39:38	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "and", "conjunction logical", "existence", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture", "triangle" ]
27	More solid black figures vs. more outline figures.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.	All small squares appearing in this problem are axis-aligned. All examples have at least one filled shape and one outline.			Mikhail M. Bongard	2023-06-16 21:36:15	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "number", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
28	More solid black circles vs. more outline circles.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.	All examples have at least two filled shapes and two outlines.			Mikhail M. Bongard	2023-06-16 21:36:23	1967-01-01 00:00:00	[ "finished", "spectrum", "traditional", "bongard", "discrete", "viceversa" ]	[ "and", "conjunction logical", "number", "outlined_filled", "color", "filled", "cluster", "texture", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
29	There are more small circles inside the figure outline than outside vs. there are fewer small circles inside the figure outline than outside.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.				Mikhail M. Bongard	2023-06-16 21:36:58	1967-01-01 00:00:00	[ "finished", "spectrum", "traditional", "bongard", "discrete", "viceversa" ]	[ "inside", "interior_exterior", "number", "shape_cluster", "cluster", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
30	A curve with one self-crossing vs. a curve without a self-crossing.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.			BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.	Mikhail M. Bongard	2023-06-17 10:44:01	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard" ]	[ "x-crossing", "x-point", "intersection", "existence" ]
31	One line vs. two lines.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.				Mikhail M. Bongard	2023-06-25 13:18:27	1967-01-01 00:00:00	[ "easy", "precise", "allsorted", "left-narrow", "right-narrow", "traditional", "bongard", "pixelperfect" ]	[ "one", "1", "two", "2", "distinguishing_crossing_curves" ]
32	A sharp projection vs. no sharp projection.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.				Mikhail M. Bongard	2022-12-27 11:36:48	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard", "notso" ]	[ "acute", "angle", "cusp", "protrusion" ]
33	Acute angle vs. no acute angle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.				Mikhail M. Bongard	2022-12-27 11:40:28	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard", "stretch" ]	[ "acute", "angle", "existence" ]
34	A large hole vs. a small hole.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.				Mikhail M. Bongard	2023-01-05 22:02:37	1967-01-01 00:00:00	[ "finished", "spectrum", "traditional", "bongard", "stable" ]	[ "hole", "size", "large", "small", "big", "texture" ]
35	The axis of the hole is parallel to the figure axis vs. the axis of the hole is perpendicular to the figure axis.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.				Mikhail M. Bongard	2022-12-27 11:38:59	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "hole", "line_slope", "same", "texture", "parallel", "perpendicular" ]
36	Triangle above circle vs. circle above triangle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.				Mikhail M. Bongard	2022-12-27 11:36:50	1967-01-01 00:00:00	[ "finished", "spectrum", "dual", "traditional", "handed", "rotate", "orderedpair", "bongard", "updown", "continuous", "viceversa" ]	[ "above_below", "triangle", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
37	Triangle above circle vs. circle above triangle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.				Mikhail M. Bongard	2022-12-27 11:40:29	1967-01-01 00:00:00	[ "finished", "spectrum", "noisy", "traditional", "bongard", "continuous", "viceversa" ]	[ "above_below", "triangle", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
38	Triangle larger than circle vs. triangle smaller than circle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.				Mikhail M. Bongard	2022-12-27 11:39:39	1967-01-01 00:00:00	[ "finished", "spectrum", "traditional", "orderedpair", "bongard", "continuous", "viceversa" ]	[ "size", "large", "small", "big", "triangle", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
39	Segments approximately parallel to each other vs. large angles between segments.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.				Mikhail M. Bongard	2022-12-27 11:39:01	1967-01-01 00:00:00	[ "finished", "traditional", "bongard", "unorderedtriplet" ]	[ "all", "line_slope", "same", "similar", "three", "3", "parallel" ]
40	Three points on a straight line vs. no three points on a straight line.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.				Mikhail M. Bongard	2022-12-27 11:36:53	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "collinear", "three", "3", "four", "4" ]
41	Outline circles on one straight line vs. outline circles not on one straight line.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.				Mikhail M. Bongard	2022-12-27 11:40:29	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "collinear", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture" ]
42	Points inside the figure outline are on a straight line vs. points inside the figure outline are not on a straight line.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.				Mikhail M. Bongard	2022-12-27 11:39:39	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "collinear", "interior_exterior", "shape_cluster", "cluster" ]
43	The vibration amplitude increases from left to right vs. the vibration amplitude decreases from left to right.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.				Mikhail M. Bongard	2022-12-27 11:39:02	1967-01-01 00:00:00	[ "finished", "dual", "leftright", "traditional", "handed", "bongard", "viceversa" ]	[ "size_increase_decrease", "larger, becoming", "smaller, becoming", "increasing", "decreasing", "horizontal", "leftward_rightward", "regular_irregular_change", "tracing_line_or_curve", "wave" ]
44	Small circles on different arcs vs. small circles on one arc.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.				Mikhail M. Bongard	2022-12-27 11:36:56	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "between", "cusp", "on_line_or_curve", "separation_of_joined_objects" ]
45	Outline figure on top of solid black figure vs. black figure on top of outline figure.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.				Mikhail M. Bongard	2022-12-27 11:40:30	1967-01-01 00:00:00	[ "finished", "dual", "traditional", "bongard", "viceversa" ]	[ "3d_front_back", "outlined_filled", "color", "filled", "objects_overlap", "overlap", "overlapping", "intersection", "texture" ]
46	Triangle on top of the circle vs. circle on top of the triangle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.				Mikhail M. Bongard	2022-12-27 11:39:39	1967-01-01 00:00:00	[ "finished", "traditional", "bongard", "viceversa" ]	[ "3d_front_back", "objects_overlap", "overlap", "overlapping", "intersection", "triangle" ]
47	Triangle inside of the circle vs. circle inside of the triangle.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.				Mikhail M. Bongard	2022-12-27 11:39:02	1967-01-01 00:00:00	[ "finished", "traditional", "bongard", "viceversa" ]	[ "inside", "triangle" ]
48	Solid dark figures above the outline figures vs. outline figures above the solid dark figures.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.				Mikhail M. Bongard	2022-12-27 11:36:59	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard", "viceversa" ]	[ "above_below", "average", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture" ]
49	Points inside the figure outline are grouped more densely than outside the contour vs. points outside the figure contour are grouped more densely than inside the contour.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.				Mikhail M. Bongard	2022-12-27 11:40:31	1967-01-01 00:00:00	[ "finished", "traditional", "bongard", "viceversa" ]	[ "inside", "interior_exterior", "near_far", "close to", "far from", "together", "feature_cluster", "shape_cluster", "cluster" ]
50	Vertical axis of symmetry vs. no axis of symmetry.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.			BP152 is the same solution (with the sides switched), using connected shapes and without black filling. BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)	Mikhail M. Bongard	2023-06-16 19:15:11	1967-01-01 00:00:00	[ "nice", "finished", "left-narrow", "traditional", "bongard", "stretch" ]	[ "symmetry_axis", "symmetry" ]
51	Two circles close to each other vs. no two circles close to each other.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.				Mikhail M. Bongard	2022-12-27 11:39:03	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard" ]	[ "near_far", "close to", "far from", "together" ]
52	Arrows pointing in different directions vs. arrows pointing in the same direction.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.				Mikhail M. Bongard	2022-12-27 11:37:02	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "arrow", "tracing_lines_or_curves_meet", "pointing_to", "tracing_line_or_curve", "imagined_point", "imagined_entity" ]
53	Inside figure has fewer angles than outside figure vs. inside figure has more angles than outside figure.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.				Mikhail M. Bongard	2023-06-16 21:37:08	1967-01-01 00:00:00	[ "finished", "spectrum", "traditional", "bongard", "discrete", "viceversa" ]	[ "inside", "number", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]
54	A cross, circle, and triangle arranged counterclockwise vs. a cross, circle, and triangle arranged clockwise.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.				Mikhail M. Bongard	2022-12-27 11:39:40	1967-01-01 00:00:00	[ "finished", "dual", "traditional", "handed", "bongard", "orderedtriplet" ]	[ "turn_orientation", "rotational_direction", "triangle", "direction" ]
55	A circle is at the left of the cavity if you look from inside the figure vs. a circle is at the right of the cavity if you look from inside the figure.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.				Mikhail M. Bongard	2022-12-27 11:39:03	1967-01-01 00:00:00	[ "finished", "dual", "traditional", "handed", "bongard" ]	[ "indentation", "notch", "on_line_or_curve", "separation_of_joined_objects", "tracing_line_or_curve", "rotational_direction", "direction" ]
56	All figures of the same color vs. figures of different colors.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.				Mikhail M. Bongard	2022-12-27 11:37:04	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "all", "outlined_filled", "color", "filled", "same_feature", "same", "texture" ]
57	Identical figures vs. figures not identical.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.			BP1222 is similar but allows the shapes to be different sizes. BP343 is about existence of a pair of identical shapes among many shapes.	Mikhail M. Bongard	2023-06-17 13:55:29	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "unorderedpair", "bongard" ]	[ "identical", "same_shape", "same" ]
58	Solid dark quadrangles are identical vs. solid dark quadrangles are different.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.				Mikhail M. Bongard	2023-06-16 20:46:51	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "identical", "outlined_filled", "color", "filled", "square", "feature_cluster", "cluster", "same_shape", "same", "texture" ]
59	Figures are similar vs. figures are not similar.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.				Mikhail M. Bongard	2022-12-27 11:39:03	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "unorderedpair", "bongard" ]	[ "similar_shape", "similar" ]
60	Some similar figures vs. no similar figures.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.				Mikhail M. Bongard	2022-12-27 11:37:06	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "similar_shape", "similar" ]
61	A line separates the crosses in half vs. a line does not separate the crosses in half.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.				Mikhail M. Bongard	2022-12-27 11:40:32	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "sides_of_line", "shape_cluster", "cluster", "same_number", "same" ]
62	Ends of the curve are far apart vs. ends of the curve are close together.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.				Mikhail M. Bongard	2022-12-27 11:39:41	1967-01-01 00:00:00	[ "nice", "finished", "spectrum", "fuzzy", "traditional", "bongard", "stable", "stretch", "continuous" ]	[ "line_or_curve_endpoint", "near_far", "close to", "far from", "together" ]
63	Shading thicker on the right side vs. shading thicker on the left side.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.				Mikhail M. Bongard	2022-12-27 11:39:04	1967-01-01 00:00:00	[ "finished", "dual", "traditional", "handed", "bongard", "viceversa" ]	[ "left_right", "curve_texture", "texture" ]
64	A cross is located on the extension of the ellipse axis vs. a circle is located on the extension of the ellipse axis.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.				Mikhail M. Bongard	2022-12-27 11:37:11	1967-01-01 00:00:00	[ "finished", "noisy", "dual", "traditional", "bongard", "orderedtriplet" ]	[ "collinear", "imagined_line_or_curve", "imagined_entity" ]
65	A set of triangles elongated horizontally vs. a set of triangles elongated vertically.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.				Mikhail M. Bongard	2022-12-27 11:40:33	1967-01-01 00:00:00	[ "finished", "spectrum", "noisy", "traditional", "rotate", "bongard", "viceversa" ]	[ "convex_hull", "elongated_compact", "horizontal", "cluster", "similar_feature", "similar", "vertical" ]
66	Unconnected circles on a horizontal line vs. unconnected circles on a vertical line.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.				Mikhail M. Bongard	2022-12-27 11:39:42	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "collinear", "horizontal", "on_line_or_curve", "shape_cluster", "cluster", "vertical" ]
67	The right branch begins at a higher point than the left branch vs. the right branch begins at a lower point than the left branch.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.				Mikhail M. Bongard	2022-12-27 11:39:04	1967-01-01 00:00:00	[ "finished", "spectrum", "precise", "dual", "leftright", "traditional", "handed", "bongard", "continuous", "viceversa" ]	[ "above_below", "branch_point", "left_right", "on_sides_of_curve", "tracing_line_or_curve" ]
68	The end of the right branch is higher than that of the left branch vs. the end of the right branch is lower than that of the left branch.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.				Mikhail M. Bongard	2022-12-27 11:37:13	1967-01-01 00:00:00	[ "finished", "traditional", "bongard", "viceversa" ]	[ "above_below", "branch_point", "line_or_curve_endpoint", "left_right", "tracing_line_or_curve" ]
69	Large black dot on the main branch vs. large black dot on a side branch.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.				Mikhail M. Bongard	2022-12-27 11:40:34	1967-01-01 00:00:00	[ "finished", "traditional", "bongard" ]	[ "line_or_curve_endpoint", "on_line_or_curve", "tracing_line_or_curve", "trunk_of_tree" ]
70	There are no side branches of the second order vs. there are side branches of the second order.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.				Mikhail M. Bongard	2022-12-27 11:39:43	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard" ]	[ "recursion", "nesting", "tracing_line_or_curve", "trunk_of_tree", "two", "2", "recursion_number" ]
71	There are inside figures of the second order vs. there are no inside figures of the second order.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.			See BP1022 for a Problem about presence of nesting.	Mikhail M. Bongard	2022-12-27 11:39:04	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard" ]	[ "inside", "recursion", "nesting", "two", "2", "recursion_number" ]
72	Ends of the curve are parallel vs. ends of the curve are perpendicular.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.				Mikhail M. Bongard	2022-12-28 16:35:44	1967-01-01 00:00:00	[ "nice", "finished", "precise", "traditional", "bongard", "ignoreimperfections", "unstable" ]	[ "slope_at_endpoint", "tracing_line_or_curve", "parallel", "perpendicular" ]
73	The long axes of the ellipse and rectangle are perpendicular vs. the long axes of the ellipse and rectangle are parallel.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 238.				Mikhail M. Bongard	2022-12-27 11:40:34	1967-01-01 00:00:00	[ "finished", "noisy", "traditional", "bongard" ]	[ "imagined_line_or_curve", "imagined_entity", "parallel", "perpendicular" ]
74	A tail grows from the obtuse end vs. a tail grows from the acute end.	M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 238.				Mikhail M. Bongard	2022-12-27 11:39:44	1967-01-01 00:00:00	[ "nice", "finished", "traditional", "bongard" ]	[ "size_increase_decrease", "larger, becoming", "smaller, becoming", "increasing", "decreasing", "tracing_line_or_curve", "imagined_line_or_curve", "imagined_entity" ]

1

Empty image vs. non-empty image.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

The first Bongard Problem. All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).

A circle fits on the right because it is not nothing.

Mikhail M. Bongard

0

2023-06-18 19:55:03

1967-01-01 00:00:00

[ "easy", "nice", "finished", "precise", "allsorted", "left-narrow", "left-finite", "world", "traditional", "left-null", "left-full", "bongard", "perfect", "pixelperfect", "unstable", "stableworld", "deformstable" ]

[ "empty", "nothing", "existence", "zero", "0" ]

2

Big vs. small.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

The meaning of "big" left intentionally vague. There are various specific ways to define size, such as diameter, minimum distance between points on edge, and size of smallest bounding circle. All examples in this Bongard Problem are single simple shapes, either outlines or solid black. All examples on the same side a...

Mikhail M. Bongard

0

2024-09-19 05:50:19

1967-01-01 00:00:00

[ "easy", "nice", "finished", "spectrum", "fuzzy", "traditional", "size", "bongard", "stable", "continuous" ]

[ "size", "large", "small", "big" ]

3

Hollow outline vs. filled in solid.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

All examples in this Bongard Problem are single simple shapes.

Mikhail M. Bongard

0

2023-06-16 20:43:59

1967-01-01 00:00:00

[ "easy", "nice", "finished", "precise", "allsorted", "world", "traditional", "bongard", "gap", "preciseworld" ]

[ "outlined_filled", "color", "filled", "texture" ]

4

Convex vs. concave.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.

All examples in this Problem are outlines of shapes or solid black shapes.

BP136 is the same solution (flipped) but with only polygonal outlines and also with extraneous dots distracting from the solution.

Mikhail M. Bongard

0

2023-06-16 20:06:35

1967-01-01 00:00:00

[ "easy", "nice", "finished", "precise", "right-narrow", "traditional", "bongard", "unstable" ]

[ "concave_convex_angle" ]

5

Is polygon vs. is smooth without straight lines or corners.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.

All examples in this Bongard Problem are outlines of shapes.

Mikhail M. Bongard

0

2022-12-28 15:44:45

1967-01-01 00:00:00

[ "easy", "nice", "finished", "traditional", "bongard", "ignoreimperfections" ]

[ "curved_straight" ]

6

Triangle vs. quadrilateral.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 215.

All examples in this Problem are outlines of polygons or solid black polygons.

BP1211 is "triangle vs. anything else".

Mikhail M. Bongard

0

2023-06-16 16:24:36

1967-01-01 00:00:00

[ "easy", "nice", "finished", "precise", "traditional", "number", "bongard", "ignoreimperfections", "preciseworld" ]

[ "number", "triangle", "three", "3", "four", "4" ]

7

Taller than wide vs. wider than tall.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.

All examples in this Bongard Problem are oblong connected figures made up of some curves. Shapes as tall as they are wide would be ambiguous.

Mikhail M. Bongard

0

2022-12-27 11:17:09

1967-01-01 00:00:00

[ "easy", "nice", "finished", "dual", "traditional", "handed", "rotate", "bongard", "stretch" ]

[ "horizontal", "line_slope", "vertical", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

8

Positioned right vs. positioned left.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.

Center of shape's x coordinate is higher than zero (where zero is the middle of the picture). All examples in this Bongard Problem are small shape outlines. This is the first Bongard Problem in which absolute positioning is relevant. Shapes close to the middle would be ambiguous.

Mikhail M. Bongard

0

2022-12-27 11:17:40

1967-01-01 00:00:00

[ "easy", "nice", "finished", "dual", "leftright", "traditional", "handed", "bongard", "boundingbox", "absoluteposition" ]

[ "absolute_position", "bounding_box", "coordinate", "left_right" ]

9

Non-wiggly outline vs. wiggly outline.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 216.

"Wiggly" means a high number of small concavities adjacent to one another all around the outline. All examples in this Bongard Problem are shape outlines. Shapes with outlines that are only wiggly within partial sections would be ambiguous. Shapes with outlines that have many medium-size concavities would be ambiguou...

Mikhail M. Bongard

0

2023-06-15 08:54:23

1967-01-01 00:00:00

[ "easy", "nice", "finished", "fuzzy", "world", "traditional", "bongard", "stable" ]

[ "curve_texture", "texture" ]

10

Approximately triangular outline vs. approximately convex quadrilateral outline.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.

All examples in this Bongard Problem are shape outlines.

Mikhail M. Bongard

0

2023-06-16 21:35:47

1967-01-01 00:00:00

[ "easy", "finished", "fuzzy", "noisy", "traditional", "number", "bongard" ]

[ "number", "three", "3", "four", "4" ]

11

Thin and elongated vs. compact.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.

All examples in this Bongard Problem are shape outlines.

Mikhail M. Bongard

0

2023-01-05 22:01:57

1967-01-01 00:00:00

[ "nice", "finished", "spectrum", "fuzzy", "world", "traditional", "bongard", "stable", "stretch" ]

[ "elongated_compact" ]

12

Thin elongated convex hull vs. compact convex hull.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 217.

All examples in this Bongard Problem are shape outlines.

Mikhail M. Bongard

0

2022-12-27 11:38:24

1967-01-01 00:00:00

[ "nice", "finished", "spectrum", "fuzzy", "traditional", "bongard", "stretch" ]

[ "convex_hull", "elongated_compact" ]

13

Tall rectangle OR wide ellipse vs. wide rectangle OR tall ellipse.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.

All examples in this Bongard Problem are outlines of ellipses or rectangles aligned to the x-y-axes.

Mikhail M. Bongard

0

2023-01-05 22:01:27

1967-01-01 00:00:00

[ "finished", "precise", "traditional", "bongard", "stretch", "preciseworld" ]

[ "or", "disjunction logical", "horizontal", "line_slope", "vertical" ]

14

All big individual figures vs. all small individual figures.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.

All examples in this Problem show one or more connected figures made up of lines. Some big shapes and some small shapes would be ambiguous.

See BP2 for the same idea using one shape.

Mikhail M. Bongard

0

2023-01-05 22:02:18

1967-01-01 00:00:00

[ "finished", "fuzzy", "traditional", "size", "bongard", "stable" ]

[ "all", "length_line_or_curve", "size", "large", "small", "big" ]

15

Closed shape outline vs. non-closed curve.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.

All examples in this Bongard Problem are non-self-intersecting curves.

Mikhail M. Bongard

0

2023-06-25 13:32:03

1967-01-01 00:00:00

[ "nice", "finished", "world", "traditional", "bongard", "unstable" ]

[ "closed_open", "hole", "loop" ]

16

Clockwise spiraling curve vs. counter-clockwise spiraling curve.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.

All examples in this Bongard Problem are non-self-intersecting spiraling curves, perhaps wiggly, perhaps with corners.

Mikhail M. Bongard

0

2023-06-16 16:44:57

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "handed", "bongard", "gap" ]

[ "turn_orientation", "tracing_line_or_curve", "rotational_direction", "direction" ]

17

Shape with a reflex corner vs. shape without a reflex corner.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.

All examples in this Bongard Problem are outlines of shapes.

Mikhail M. Bongard

0

2022-12-27 11:40:26

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "acute", "angle", "indentation", "notch" ]

18

"Pinched" shape (drastically thinner somewhere in the middle than on the ends) vs. non-pinched shape.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 219.

All examples in this Bongard Problem are oblong outlines of shapes.

Mikhail M. Bongard

0

2022-12-27 11:39:38

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "neck_narrowing" ]

19

Horizontal pinch vs. vertical pinch.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.

All examples in this Bongard Problem are outlines of shapes. More specifically, all examples have a thin horizontal or vertical bridge in the middle connecting two wide ends.

Mikhail M. Bongard

0

2022-12-27 11:38:43

1967-01-01 00:00:00

[ "finished", "dual", "traditional", "rotate", "bongard" ]

[ "horizontal", "neck_narrowing", "vertical" ]

20

Both dots touching same bulb vs. dots on opposite bulbs.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.

All examples in this Bongard Problem are outlines of smooth shapes with a pinch in the middle and with two tiny black circles attached to the outside of the shape (tangent). A shape with either dot tangent to the the valley section would be ambiguous.

Mikhail M. Bongard

0

2022-12-27 11:36:17

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard" ]

[ "near_far", "close to", "far from", "together", "neck_narrowing", "separation_of_joined_objects" ]

21

Small shape present vs. all shapes large.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 220.

All examples in this problem include three or fewer outlines of circles and (non-skinny) triangles.

Mikhail M. Bongard

0

2022-12-27 11:40:27

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "existence", "size", "large", "small", "big" ]

22

All shapes approximately the same size vs. shapes of different size.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.

All examples in this problem include three or fewer outlines of circles, (near-square) quadrilaterals and (non-skinny) triangles.

Mikhail M. Bongard

0

2022-12-27 11:39:38

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "all", "average", "size", "large", "small", "big" ]

23

One vs. two figures.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.

All examples in this Problem comprise one or two shape outlines.

Mikhail M. Bongard

0

2022-12-28 16:29:06

1967-01-01 00:00:00

[ "easy", "nice", "finished", "precise", "world", "traditional", "number", "bongard", "gap" ]

[ "number", "one", "1", "two", "2" ]

24

A circle vs. no circle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 221.

All small squares appearing in this problem are axis-aligned.

Mikhail M. Bongard

0

2023-06-16 16:28:00

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "circle", "existence" ]

25

Black figure is a triangle vs. black figure is a circle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.

All small squares appearing in this problem are axis-aligned.

Mikhail M. Bongard

0

2022-12-27 11:40:27

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture", "triangle" ]

26

Solid black triangle vs. no solid black triangle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.

Mikhail M. Bongard

0

2022-12-27 11:39:38

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "and", "conjunction logical", "existence", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture", "triangle" ]

27

More solid black figures vs. more outline figures.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 222.

All small squares appearing in this problem are axis-aligned. All examples have at least one filled shape and one outline.

Mikhail M. Bongard

0

2023-06-16 21:36:15

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "number", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

28

More solid black circles vs. more outline circles.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.

All examples have at least two filled shapes and two outlines.

Mikhail M. Bongard

0

2023-06-16 21:36:23

1967-01-01 00:00:00

[ "finished", "spectrum", "traditional", "bongard", "discrete", "viceversa" ]

[ "and", "conjunction logical", "number", "outlined_filled", "color", "filled", "cluster", "texture", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

29

There are more small circles inside the figure outline than outside vs. there are fewer small circles inside the figure outline than outside.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.

Mikhail M. Bongard

0

2023-06-16 21:36:58

1967-01-01 00:00:00

[ "finished", "spectrum", "traditional", "bongard", "discrete", "viceversa" ]

[ "inside", "interior_exterior", "number", "shape_cluster", "cluster", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

30

A curve with one self-crossing vs. a curve without a self-crossing.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 223.

BP1232 is almost exactly the same, but allowing for multiple curves and multiple self-crossings.

Mikhail M. Bongard

0

2023-06-17 10:44:01

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard" ]

[ "x-crossing", "x-point", "intersection", "existence" ]

31

One line vs. two lines.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.

Mikhail M. Bongard

0

2023-06-25 13:18:27

1967-01-01 00:00:00

[ "easy", "precise", "allsorted", "left-narrow", "right-narrow", "traditional", "bongard", "pixelperfect" ]

[ "one", "1", "two", "2", "distinguishing_crossing_curves" ]

32

A sharp projection vs. no sharp projection.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.

Mikhail M. Bongard

0

2022-12-27 11:36:48

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard", "notso" ]

[ "acute", "angle", "cusp", "protrusion" ]

33

Acute angle vs. no acute angle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 224.

Mikhail M. Bongard

0

2022-12-27 11:40:28

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard", "stretch" ]

[ "acute", "angle", "existence" ]

34

A large hole vs. a small hole.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.

Mikhail M. Bongard

0

2023-01-05 22:02:37

1967-01-01 00:00:00

[ "finished", "spectrum", "traditional", "bongard", "stable" ]

[ "hole", "size", "large", "small", "big", "texture" ]

35

The axis of the hole is parallel to the figure axis vs. the axis of the hole is perpendicular to the figure axis.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.

Mikhail M. Bongard

0

2022-12-27 11:38:59

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "hole", "line_slope", "same", "texture", "parallel", "perpendicular" ]

36

Triangle above circle vs. circle above triangle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 225.

Mikhail M. Bongard

0

2022-12-27 11:36:50

1967-01-01 00:00:00

[ "finished", "spectrum", "dual", "traditional", "handed", "rotate", "orderedpair", "bongard", "updown", "continuous", "viceversa" ]

[ "above_below", "triangle", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

37

Triangle above circle vs. circle above triangle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.

Mikhail M. Bongard

0

2022-12-27 11:40:29

1967-01-01 00:00:00

[ "finished", "spectrum", "noisy", "traditional", "bongard", "continuous", "viceversa" ]

[ "above_below", "triangle", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

38

Triangle larger than circle vs. triangle smaller than circle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.

Mikhail M. Bongard

0

2022-12-27 11:39:39

1967-01-01 00:00:00

[ "finished", "spectrum", "traditional", "orderedpair", "bongard", "continuous", "viceversa" ]

[ "size", "large", "small", "big", "triangle", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

39

Segments approximately parallel to each other vs. large angles between segments.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 226.

Mikhail M. Bongard

0

2022-12-27 11:39:01

1967-01-01 00:00:00

[ "finished", "traditional", "bongard", "unorderedtriplet" ]

[ "all", "line_slope", "same", "similar", "three", "3", "parallel" ]

40

Three points on a straight line vs. no three points on a straight line.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.

Mikhail M. Bongard

0

2022-12-27 11:36:53

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "collinear", "three", "3", "four", "4" ]

41

Outline circles on one straight line vs. outline circles not on one straight line.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.

Mikhail M. Bongard

0

2022-12-27 11:40:29

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "collinear", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture" ]

42

Points inside the figure outline are on a straight line vs. points inside the figure outline are not on a straight line.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 227.

Mikhail M. Bongard

0

2022-12-27 11:39:39

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "collinear", "interior_exterior", "shape_cluster", "cluster" ]

43

The vibration amplitude increases from left to right vs. the vibration amplitude decreases from left to right.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.

Mikhail M. Bongard

0

2022-12-27 11:39:02

1967-01-01 00:00:00

[ "finished", "dual", "leftright", "traditional", "handed", "bongard", "viceversa" ]

[ "size_increase_decrease", "larger, becoming", "smaller, becoming", "increasing", "decreasing", "horizontal", "leftward_rightward", "regular_irregular_change", "tracing_line_or_curve", "wave" ]

44

Small circles on different arcs vs. small circles on one arc.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.

Mikhail M. Bongard

0

2022-12-27 11:36:56

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "between", "cusp", "on_line_or_curve", "separation_of_joined_objects" ]

45

Outline figure on top of solid black figure vs. black figure on top of outline figure.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 228.

Mikhail M. Bongard

0

2022-12-27 11:40:30

1967-01-01 00:00:00

[ "finished", "dual", "traditional", "bongard", "viceversa" ]

[ "3d_front_back", "outlined_filled", "color", "filled", "objects_overlap", "overlap", "overlapping", "intersection", "texture" ]

46

Triangle on top of the circle vs. circle on top of the triangle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.

Mikhail M. Bongard

0

2022-12-27 11:39:39

1967-01-01 00:00:00

[ "finished", "traditional", "bongard", "viceversa" ]

[ "3d_front_back", "objects_overlap", "overlap", "overlapping", "intersection", "triangle" ]

47

Triangle inside of the circle vs. circle inside of the triangle.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.

Mikhail M. Bongard

0

2022-12-27 11:39:02

1967-01-01 00:00:00

[ "finished", "traditional", "bongard", "viceversa" ]

[ "inside", "triangle" ]

48

Solid dark figures above the outline figures vs. outline figures above the solid dark figures.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 229.

Mikhail M. Bongard

0

2022-12-27 11:36:59

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard", "viceversa" ]

[ "above_below", "average", "outlined_filled", "color", "filled", "feature_cluster", "cluster", "texture" ]

49

Points inside the figure outline are grouped more densely than outside the contour vs. points outside the figure contour are grouped more densely than inside the contour.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.

Mikhail M. Bongard

0

2022-12-27 11:40:31

1967-01-01 00:00:00

[ "finished", "traditional", "bongard", "viceversa" ]

[ "inside", "interior_exterior", "near_far", "close to", "far from", "together", "feature_cluster", "shape_cluster", "cluster" ]

50

Vertical axis of symmetry vs. no axis of symmetry.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.

BP152 is the same solution (with the sides switched), using connected shapes and without black filling. BP1206 was created to be a slightly different version of this: "vertical axis of symmetry vs. no vertical axis of symmetry." (That less specific solution fits this Bongard Problem as well.)

Mikhail M. Bongard

0

2023-06-16 19:15:11

1967-01-01 00:00:00

[ "nice", "finished", "left-narrow", "traditional", "bongard", "stretch" ]

[ "symmetry_axis", "symmetry" ]

51

Two circles close to each other vs. no two circles close to each other.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 230.

Mikhail M. Bongard

0

2022-12-27 11:39:03

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard" ]

[ "near_far", "close to", "far from", "together" ]

52

Arrows pointing in different directions vs. arrows pointing in the same direction.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.

Mikhail M. Bongard

0

2022-12-27 11:37:02

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "arrow", "tracing_lines_or_curves_meet", "pointing_to", "tracing_line_or_curve", "imagined_point", "imagined_entity" ]

53

Inside figure has fewer angles than outside figure vs. inside figure has more angles than outside figure.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.

Mikhail M. Bongard

0

2023-06-16 21:37:08

1967-01-01 00:00:00

[ "finished", "spectrum", "traditional", "bongard", "discrete", "viceversa" ]

[ "inside", "number", "quantity_comparison", "more", "less", "greater", "lesser", "greater than", "less than", "fewer" ]

54

A cross, circle, and triangle arranged counterclockwise vs. a cross, circle, and triangle arranged clockwise.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 231.

Mikhail M. Bongard

0

2022-12-27 11:39:40

1967-01-01 00:00:00

[ "finished", "dual", "traditional", "handed", "bongard", "orderedtriplet" ]

[ "turn_orientation", "rotational_direction", "triangle", "direction" ]

55

A circle is at the left of the cavity if you look from inside the figure vs. a circle is at the right of the cavity if you look from inside the figure.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.

Mikhail M. Bongard

0

2022-12-27 11:39:03

1967-01-01 00:00:00

[ "finished", "dual", "traditional", "handed", "bongard" ]

[ "indentation", "notch", "on_line_or_curve", "separation_of_joined_objects", "tracing_line_or_curve", "rotational_direction", "direction" ]

56

All figures of the same color vs. figures of different colors.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.

Mikhail M. Bongard

0

2022-12-27 11:37:04

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "all", "outlined_filled", "color", "filled", "same_feature", "same", "texture" ]

57

Identical figures vs. figures not identical.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 232.

BP1222 is similar but allows the shapes to be different sizes. BP343 is about existence of a pair of identical shapes among many shapes.

Mikhail M. Bongard

0

2023-06-17 13:55:29

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "unorderedpair", "bongard" ]

[ "identical", "same_shape", "same" ]

58

Solid dark quadrangles are identical vs. solid dark quadrangles are different.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.

Mikhail M. Bongard

0

2023-06-16 20:46:51

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "identical", "outlined_filled", "color", "filled", "square", "feature_cluster", "cluster", "same_shape", "same", "texture" ]

59

Figures are similar vs. figures are not similar.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.

Mikhail M. Bongard

0

2022-12-27 11:39:03

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "unorderedpair", "bongard" ]

[ "similar_shape", "similar" ]

60

Some similar figures vs. no similar figures.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 233.

Mikhail M. Bongard

0

2022-12-27 11:37:06

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "similar_shape", "similar" ]

61

A line separates the crosses in half vs. a line does not separate the crosses in half.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.

Mikhail M. Bongard

0

2022-12-27 11:40:32

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "sides_of_line", "shape_cluster", "cluster", "same_number", "same" ]

62

Ends of the curve are far apart vs. ends of the curve are close together.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.

Mikhail M. Bongard

0

2022-12-27 11:39:41

1967-01-01 00:00:00

[ "nice", "finished", "spectrum", "fuzzy", "traditional", "bongard", "stable", "stretch", "continuous" ]

[ "line_or_curve_endpoint", "near_far", "close to", "far from", "together" ]

63

Shading thicker on the right side vs. shading thicker on the left side.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 234.

Mikhail M. Bongard

0

2022-12-27 11:39:04

1967-01-01 00:00:00

[ "finished", "dual", "traditional", "handed", "bongard", "viceversa" ]

[ "left_right", "curve_texture", "texture" ]

64

A cross is located on the extension of the ellipse axis vs. a circle is located on the extension of the ellipse axis.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.

Mikhail M. Bongard

0

2022-12-27 11:37:11

1967-01-01 00:00:00

[ "finished", "noisy", "dual", "traditional", "bongard", "orderedtriplet" ]

[ "collinear", "imagined_line_or_curve", "imagined_entity" ]

65

A set of triangles elongated horizontally vs. a set of triangles elongated vertically.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.

Mikhail M. Bongard

0

2022-12-27 11:40:33

1967-01-01 00:00:00

[ "finished", "spectrum", "noisy", "traditional", "rotate", "bongard", "viceversa" ]

[ "convex_hull", "elongated_compact", "horizontal", "cluster", "similar_feature", "similar", "vertical" ]

66

Unconnected circles on a horizontal line vs. unconnected circles on a vertical line.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 235.

Mikhail M. Bongard

0

2022-12-27 11:39:42

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "collinear", "horizontal", "on_line_or_curve", "shape_cluster", "cluster", "vertical" ]

67

The right branch begins at a higher point than the left branch vs. the right branch begins at a lower point than the left branch.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.

Mikhail M. Bongard

0

2022-12-27 11:39:04

1967-01-01 00:00:00

[ "finished", "spectrum", "precise", "dual", "leftright", "traditional", "handed", "bongard", "continuous", "viceversa" ]

[ "above_below", "branch_point", "left_right", "on_sides_of_curve", "tracing_line_or_curve" ]

68

The end of the right branch is higher than that of the left branch vs. the end of the right branch is lower than that of the left branch.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.

Mikhail M. Bongard

0

2022-12-27 11:37:13

1967-01-01 00:00:00

[ "finished", "traditional", "bongard", "viceversa" ]

[ "above_below", "branch_point", "line_or_curve_endpoint", "left_right", "tracing_line_or_curve" ]

69

Large black dot on the main branch vs. large black dot on a side branch.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 236.

Mikhail M. Bongard

0

2022-12-27 11:40:34

1967-01-01 00:00:00

[ "finished", "traditional", "bongard" ]

[ "line_or_curve_endpoint", "on_line_or_curve", "tracing_line_or_curve", "trunk_of_tree" ]

70

There are no side branches of the second order vs. there are side branches of the second order.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.

Mikhail M. Bongard

0

2022-12-27 11:39:43

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard" ]

[ "recursion", "nesting", "tracing_line_or_curve", "trunk_of_tree", "two", "2", "recursion_number" ]

71

There are inside figures of the second order vs. there are no inside figures of the second order.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.

See BP1022 for a Problem about presence of nesting.

Mikhail M. Bongard

0

2022-12-27 11:39:04

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard" ]

[ "inside", "recursion", "nesting", "two", "2", "recursion_number" ]

72

Ends of the curve are parallel vs. ends of the curve are perpendicular.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 237.

Mikhail M. Bongard

0

2022-12-28 16:35:44

1967-01-01 00:00:00

[ "nice", "finished", "precise", "traditional", "bongard", "ignoreimperfections", "unstable" ]

[ "slope_at_endpoint", "tracing_line_or_curve", "parallel", "perpendicular" ]

73

The long axes of the ellipse and rectangle are perpendicular vs. the long axes of the ellipse and rectangle are parallel.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 238.

Mikhail M. Bongard

0

2022-12-27 11:40:34

1967-01-01 00:00:00

[ "finished", "noisy", "traditional", "bongard" ]

[ "imagined_line_or_curve", "imagined_entity", "parallel", "perpendicular" ]

74

A tail grows from the obtuse end vs. a tail grows from the acute end.

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 238.

Mikhail M. Bongard

0

2022-12-27 11:39:44

1967-01-01 00:00:00

[ "nice", "finished", "traditional", "bongard" ]

[ "size_increase_decrease", "larger, becoming", "smaller, becoming", "increasing", "decreasing", "tracing_line_or_curve", "imagined_line_or_curve", "imagined_entity" ]