Solutions of Bongard Problems

that appear in the index of all Bongard Problems in the author’s cognitive science pages

Note: the solutions of Bongard Problems, below, are stated as have been supplied by their respective designers (the designer can be seen by clicking on the linked BP). The exceptions are BP’s #101–156, for which Hofstadter did not supply solutions, so those have been added by the author of this page. The same applies to the occasional alternative solution for a few BP’s.

Bongard Problem # Left-side Rule Right-side Rule
BP#1 Empty picture Not empty picture
BP#2 Large figures Small figures
BP#3 Outline figures Solid figures
BP#4 Convex figures Nonconvex figures
BP#5 Polygons Curvilinear figures
BP#6 Triangles Quadrangles
BP#7 Figures elongated vertically Figures elongated horizontally
BP#8 Figures on the right side Figures on the left side
BP#9 Smooth contour figures Twisting contour figures
BP#10 Triangles Quadrangles
BP#11 Elongated figures Compact figures
BP#12 Convex hull of figure elongated Convex hull of figure compact
BP#13 Vertical rectangles or horizontal ellipses Vertical ellipses or horizontal rectangles
BP#14 Large total line length Small total line length
BP#15 Closed lines Open lines
BP#16 Spiral curls counterclockwise Spiral curls clockwise
BP#17 An acute angle directed inward No angle directed inward
BP#18 A neck No neck
BP#19 Neck horizontal Neck vertical
BP#20 Points located on one side of the neck Points located on both sides of the neck
BP#21 Small figure present No small figure present
BP#22 Areas of figures approximately equal Areas of figures differ greatly
BP#23 One figure Two figures
BP#24 A circle No circle
BP#25 Black figure is a triangle Black figure is a circle
BP#26 Solid black triangle No solid black triangle
BP#27 More solid black figures More outline figures
BP#28 More solid black circles More outline circles
BP#29 There are more small circles inside the figure outline than outside There are fewer small circles inside the figure outline than outside
BP#30 A line with a self-crossing A line without a self-crossing
BP#31 One line Two lines
BP#32 A sharp projection No sharp projection
BP#33 Acute angle No acute angle
BP#34 A large hole A small hole
BP#35 The axis of the hole is parallel to the figure axis The axis of the hole is perpendicular to the figure axis
BP#36 Triangle above circle Circle above triangle
BP#37 Triangle above circle Circle above triangle
BP#38 Triangle larger than circle Triangle smaller than circle
BP#39 Segments almost parallel to each other Large angles between segments
BP#40 Three points on a straight line No three points on a straight line
BP#41 Outline circles on one straight line Outline circles not on one straight line
BP#42 Points inside the figure outline are on a straight line Points inside the figure outline are not on a straight line
BP#43 The vibration amplitude increases from left to right The vibration amplitude decreases from left to right
BP#44 Small circles on different arcs Small circles on one arc
BP#45 Outline figure on top of solid black figure Black figure on top of outline figure
BP#46 Triangle on top of the circle Circle on top of the triangle
BP#47 Triangle inside of the circle Circle inside of the triangle
BP#48 Solid dark figures above the outline figures Outline figures above the solid dark figures
BP#49 Points inside the figure outline are grouped more densely than outside the contour Points outside the figure contour are grouped more densely than inside the contour
BP#50 Axes of symmetry No axes of symmetry
BP#51 Two circles close to each other No two circles close to each other
BP#52 Arrows pointing in different directions Arrows pointing in the same direction
BP#53 Inside figure has fewer angles than outside figure Inside figure has more angles than outside figure
BP#54 A cross, circle, and triangle arranged counterclockwise A cross, circle, and triangle arranged clockwise
BP#55 A circle is at the left of the cavity if you look from inside the figure A circle is at the right of the cavity if you look from inside the figure
BP#56 All figures of the same color Figures of different colors
BP#57 Identical figures Figures not identical
BP#58 Solid dark quadrangles are identical Solid dark quadrangles are different
BP#59 Figures are similar Figures are not similar
BP#60 Some similar figures No similar figures
BP#61 A line separates the crosses in half A line does not separate the crosses in half
BP#62 Ends of the curve are far apart Ends of the curve are close together
BP#63 Shading thicker on the right side Shading thicker on the left side
BP#64 A cross is located on the extension of the ellipse axis A circle is located on the extension of the ellipse axis
BP#65 A set of triangles elongated horizontally A set of triangles elongated vertically
BP#66 Unconnected circles on a horizontal line Unconnected circles on a vertical line
BP#67 The right branch begins at a higher point than the left branch The right branch begins at a lower point than the left branch
BP#68 The end of the right branch is higher than that of the left branch The end of the right branch is lower than that of the left branch
BP#69 Large black dot on the main branch Large black dot on a side branch
BP#70 There are no side branches of the second order There are side branches of the second order
BP#71 There are inside figures of the second order There are no inside figures of the second order
BP#72 Ends of the curve are parallel Ends of the curve are perpendicular
BP#73 The long axes of the ellipse and rectangle are perpendicular The long axes of the ellipse and rectangle are parallel
BP#74 A tail grows from the obtuse end A tail grows from the acute end
BP#75 Triangle located at the concave side of an arc Triangle located at the convex side of an arc
BP#76 Long sides concave Long sides convex
BP#77 Angle divided in half Angle not divided in half
BP#78 Extensions of segments cross at one point Extensions of segments do not cross at one point
BP#79 A dark circle is closer to the outline circle than to the triangle A dark circle is closer to the triangle than to the outline circle
BP#80 Points located at the same distances from a cross Points located at different distances from a cross
BP#81 Dark figures can be divided from outline figures by a straight line
alternatively:
Convex hulls of filled and outlined figures overlap		 Dark figures are impossible to separate
alternatively:
Convex hulls of filled and outlined figures do not overlap
BP#82 The convex hull of the crosses forms an equilateral triangle The convex hull of the crosses does not form an equilateral triangle
BP#83 A circle is inside of a figure made by crosses A circle is outside of a figure made by crosses
BP#84 A quadrangle is outside of a figure made by circles A quadrangle is inside of a figure made by circles
BP#85 Three parts Five parts
BP#86 Three parts Five parts
BP#87 Four parts Five parts
BP#88 Three parts Five parts
BP#89 Three parts Five parts
BP#90 Three parts Four parts
BP#91 Three identical elements Four identical elements
BP#92 The chain does not branch The chain branches
BP#93 Branches at outlined circle Branches at solid dark circle
BP#94 Solid dark circle not at end Solid dark circle at end
BP#95 Vertical hatched lines Horizontal hatched lines
BP#96 Triangles Quadrangles
BP#97 Triangles Circles
BP#98 Triangles Quadrangles
BP#99 Outlines made by triangles and circles intersect Outlines made by triangles and circles do not intersect
BP#100 The letter А The letter Б
BP#101 Parallel dents Perpendicular dents
BP#102 Internal arrows point outward Internal arrows point inward
BP#103 Isosceles triangle Scalene triangle
BP#104 One circle passes through the center of the other circle No circle passes through the center of the other circle
BP#105 Ends of line point to the same direction Ends of line point to opposite directions
BP#106 Negative slope Positive slope
BP#107 Three simple lines Three complex lines
BP#108 Petals taper off Petals thicken
BP#109 Circle on the right of the box Circle on the left of the box
BP#110 Four out of five objects are circles Never four out of five objects are circles
BP#111 Middle shape is a triangle Middle shape is not a triangle
BP#112 X-coordinates of dots are equidistant Y-coordinates of dots are equidistant
BP#113 T-like junction Y-like junction
BP#114 Four X-like points Two X-like points
BP#115 Innermost shape is reachable from the outermost one Innermost shape is unreachable from the outermost one
BP#116 Polygon stands on side Polygon stands on vertex
BP#117 Triangle points to center of circle Triangle does not point to center of circle
BP#118 No cycle A cycle exists
BP#119 A small correction will result into a single circle No small correction will result into a single circle
BP#120 All turns are in one direction
alternatively:
Rectangular loop exists		 Turns are not all in one direction
alternatively:
No rectangular loop
BP#121 Circle: VV; square: VΛ; triangle: ΛΛ; blank: ΛV Circle: ΛΛ; square: ΛV; triangle: VV; blank: VΛ
BP#122 Line divides interior into two regions Not so
BP#123 Similar shapes Dissimilar shapes
BP#124 Similar textures Dissimilar textures
BP#125 One protrusion and one indentation of the same shape Not so
BP#126 One large and one small object Not so
BP#127 Exactly one circle Not exactly one circle
BP#128 Same objects inside and outside the large shape Not same objects inside and outside the large shape
BP#129 Indentation on protrusion Indentation on indentation
BP#130 Closed region is made of curves if “flaws” are ignored Closed region is a polygon if “flaws” are ignored
BP#131 Dots are vertices of a parallelogram Dots are not vertices of a parallelogram
BP#132 Dots are vertices of a triangle standing on a side Dots are vertices of a triangle standing on a vertex
BP#133 Dots collinear with center of circle Dots not collinear with center of circle
BP#134 Circle centers are collinear Circle centers are not collinear
BP#135 Circles on same side of curve Circles on different sides of curves
BP#136 Concave shape Convex shape
BP#137 Dots equal in number to the sides of the closed region Dots unequal in number to the sides of the closed region
BP#138 No dot well within the convex hull At least one dot well within the convex hull
BP#139 Similar components that change regularly Not so
BP#140 One large shape and two smaller identical ones Not so
BP#141 Two clusters of three and two objects each One cluster of three objects and two different objects
BP#142 Two clusters of three and two that are adjacent Two clusters of three and two that are not adjacent
BP#143 Two clusters of three and two Two clusters of four and one
BP#144 Two clusters of three and two but sharing a property
alternatively:
Different features yield different 3-2 splits		 Two clusters of three and two, separable
alternatively:
Different features yield the same 3-2 split
BP#145 Two clusters of four and one, the four are of same kind
alternatively:
Different features yield same 4-1 split		 Two clusters of four and one, the four are three and one
alternatively:
Different features yield different 4-1 splits
BP#146 A shape contains a square if and only if it is a circle A shape contains a square if and only if it is a triangle
BP#147 Two clusters of three and two, the two are vertical Two clusters of three and two, the two are horizontal
BP#148 A little less than a regular shape A little more than a regular shape
BP#149 Lone square Lone circle
BP#150 Odd number of squares Even number of squares
BP#151 If the circle closest to the cross is removed, the rest form an equilateral triangle Not so
BP#152 No vertical axis of symmetry Vertical axis of symmetry
BP#153 Predominance of curves and hook-like endings Predominance of straight lines and staple-like endings
BP#154 Wedged endings Rounded endings
BP#155 Curves are longer than straight lines Curves are shorter than straight lines
BP#156 Three spatially separated clusters Two spatially separated clusters
BP#157 White background Black background
BP#158 Some slope Another slope
BP#159 Two clusters of 2+3, middle shape must be seen as rectangle Two clusters of 2+3, middle shape must be seen as piece of straight line
BP#160 Quadrilateral that is nearly a triangle Typical quadrilateral
BP#161 Midpoints are collinear Midpoints are not collinear
BP#162 Every other side, if extended, passes through one point Not so
BP#163 Line connecting small shapes does not intersect large one Line connecting small shapes intersects large one
BP#164 Number of objects is one less than sides Number of objects is one more than sides
BP#165 Line perpendicular to one side of the object Line parallel to one side of the object
BP#166 Two clusters of dots Three clusters of dots
BP#167 Every cluster has two clusters of dots Every cluster has three clusters of dots
BP#168 Bulky interior, if closed Narrow interior, if closed
BP#169 Two clusters of different numbers of elements Two clusters of equal number of elements
BP#170 Π-like shape X-like shape
BP#171 Angle bisectors meet at the incenter Perpendicular bisectors meet at the orthocenter
BP#172 Radially symmetric Not radially symmetric
BP#173 Small variance of slopes Large variance of slopes
BP#174 Convex central interior Concave central interior
BP#175 Small object can glide in the bay Small object cannot glide in the bay
BP#176 Line that connects dots avoiding obstacles is short Line that connects dots avoiding obstacles is long
BP#177 All interiors are convex At least one concave interior
BP#178 Center of circle in triangle perpendicular to the other two Not so
BP#179 Object thinner at top Object thicker at top
BP#180 Black region narrows at the boundary or black/white Black region widens at the boundary or black/white
BP#181 One concavity Two concavities
BP#182 Concave if proximal points are connected Convex if proximal points are connected
BP#183 Same curvature close to the middle
alternative expression of the same idea:
Tangent near the middle leaves curve on the same side		 Change of curvature close to the middle
alternative expression of the same idea:
Tangent near the middle leaves curve on opposite sides
BP#184 Curve is smooth close to the middle Curve zigzags close to the middle
BP#185 Curve with two complex parts Curve with three complex parts
BP#186 Object made of objects Object made of objects made of objects
BP#187 Sides of parts are one more than sides of whole Sides of parts are one less than sides of whole
BP#188 Shape of whole different from shape of parts Shape of whole same as shape of parts
BP#189 All clusters are made of objects of the same texture Not all clusters are made of objects of the same texture
BP#190 All connected objects have the same texture Some connected objects have different textures
BP#191 Orifice on the left Orifice on the right
BP#192 Elongated vertically Elongated horizontally
BP#193 “Ghost” triangle “Ghost” rectangle
BP#194 Background is a parallelogram Background is a triangle
BP#195 Bottom object in front of top objects in 3-D Bottom object behind top objects in 3-D
BP#196 Light-colored texture Dark-colored texture
BP#197 Some style (font) Another style (font)
BP#198 Stays in
alternative lower-level expression of the same idea:
One end of the chain is inside the large shape		 Escapes
alternative lower-level expression of the same idea:
Both ends of the chain are outside the large shape
BP#199 Stays put
alternative lower-level expression of the same idea:
Vertical from barycenter intersects the base of the object		 Tumbles
alternative lower-level expression of the same idea:
Vertical from barycenter avoids the base of the object
BP#200 Bongard Problem with solution based on features Bongard Problem with solution based on numerosity
BP#201 Two of the shapes make tiles along their border lines Not so
BP#202 Even number Odd number
BP#203 Prime number Composite number
BP#204 Five Four
BP#205 Two clusters of two elements each Not so
BP#206 Curve ends in a roughly up or down direction Curve ends in a roughly left or right direction
BP#207 Curve ends on the left part of the box Curve ends on the right part of the box
BP#208 All curves spiral counterclockwise, starting from maximum curvature All curves spiral clockwise, starting from maximum curvature
BP#209 No objects are centered at the center of the box One object is centered at the center of the box
BP#210 Part of at least one object is out of box All objects are within the box
BP#211 More black than white More white than black
BP#212 No dot is too far apart from another dot At least one dot is far apart from all other dots
BP#213 Curve intersects itself at the point of greatest curvature Not so
BP#214 “Smiley face” Not a "smiley face”
BP#215 “Mouth” concave upwards “Mouth” convex upwards
BP#216 “Ink tip” (non-homogeneous line) “Marker tip” (homogeneous line)
BP#217 Perfectly drawn lines Imperfectly drawn lines
BP#218 Something is missing in the sequence Nothing is missing in the sequence
BP#219 Parallel curves Non-parallel curves
BP#220 One cluster Two clusters
BP#221 No small square at the end of any curve
alternatively:
Curves with a 3-D feeling		 Curve ends at a small square
alternatively:
Flat (2-D) curves
BP#222 Border of black rectangle is incomplete Border of black rectangle is complete
BP#223 Large black region if completed is a circle Large black region if completed is an ellipse
BP#224 Diametrically opposite objects affect similarly the large black circular region Not so
BP#225 Low contrast
alternative lower-level expression of the same idea:
No fully black region		 High contrast
alternative lower-level expression of the same idea:
At least one fully black region
BP#226 What comes out of black circle has a clockwise direction Not so
BP#227 Dots touch each other if and only if no large region touches the edges of the box Dots don’t touch each other if and only if no large region touches the edges of the box
BP#228 After rotating so that the longest line is horizontal, there is a “left arm” raised and a “weight” down After rotating so that the longest line is horizontal, there is a “left arm” down and a “weight” raised
BP#229 When the objects are rotated and their dots are overlapped and eliminated, they form three-square-tall structures with columns of the same color Not so
Explanation / justification of BP#229 by its creator:

Long (doubly sized) objects are purines (A & G).
Short objects are pyrimidines (C & T).
Black are those forming triple Hbond (G and C).
White are those forming double Hbond (A & T).

On the left we have “matching codes”, i.e., bases, doublets or triplets that, when rotated, can pair correctly (A with T, G with C), binding the two “strands”.

On the right we have objects that no matter how they are rotated they do not pair correctly (because of bumps, wrong color codes, etc).
BP#230 The sum of vertices, line ends, and dots is 7 Not so
BP#231 Five concavities Not five concavities
BP#232 Box divided into six areas Box divided into four areas
BP#233 Lines plus triangles equal stars Lines minus triangles equal stars
BP#234 Circle falls by gravity on the right half of box if let loose Circle falls by gravity on the left half of box if let loose
BP#235 The “rope”, if extended, reaches the other ball The “rope”, if extended, does not reach the other ball
BP#236 Texture with stripy squiggle Texture with blotchy squiggle
BP#237 Upper central line appears shorter than lower central line Upper central line appears longer than lower central line
BP#238 C-like curves point to the same direction C-like curves point to opposite directions
BP#239 Straight line parallel to line joining the ends of curve
alternatively:
Sliding the straight line suitably can make a closed area		 Straight line perpendicular to line joining the ends of curve
alternatively:
Not so
BP#240 Straight line joining the curve ends does not cut the curve Straight line joining the curve ends intersects the curve
BP#241 Circumference shorter than length of everything else Circumference longer than length of everything else
BP#242 Convex hull is a square Convex hull is not a square
BP#243 Triangle closer to box corner than any of the circles Not so
BP#244 Scanning left-to-right, top-to-bottom, each filled box is separated from the next filled box by the same number of empty boxes Not so
BP#245 Can be completed to be made into a rectangle Cannot be completed to be made into a rectangle
BP#246 Equal numbers of straight lines and continuous curves Unequal numbers of straight lines and continuous curves
BP#247 Five straight or curved lines Not five straight or curved lines
BP#248 Dashed lines inside solid shape make an identical but slightly smaller shape, “parallel” to the one outside Not so
BP#249 Dashed lines form the same shape centered inside Not so
BP#250 Tetrahedron projected on the box plane
alternative lower-level expression of the same idea:
Four points interconnected with straight lines where one of the points might lie on an edge		 Not so
BP#251 Tetrahedron projected on the box plane Not so
BP#252 Impossible solid in 3-D Possible solid in 3-D
BP#253 Prime number
solution without using the arithmetic concept of primality:
It is impossible to create subgroups all of which have the same number of two-or-more identically shaped objects		 Composite number
solution without using the arithmetic concept of primality:
It is possible to create subgroups all of which have the same number of two-or-more identically shaped objects
BP#254 Circle and two vertices are collinear No two vertices and the circle are collinear
BP#255 Three pairs of parallel and non-collinear pieces of straight lines, each pair with a different slope Not so
BP#256 Each large circle closer to a small circle than a large one, and each small circle closer to a large one than a small one Not so
BP#257 The distance from the center of the line to the bottom of the square is the same as the distance from the dot to the right edge of the square Not so
BP#258 Objects identical after mirroring horizontally Objects identical after mirroring vertically
BP#259 Two identical overlapping objects of which the top is rotated slightly clockwise Not so
BP#260 Squares are either all empty or all contain something Not so
BP#261 Straight lines that join filled and outlined circles intersect Straight lines that join filled and outlined circles do not intersect
BP#262 Exactly one point where lines bend at an angle Not exactly one point where lines bend at an angle
BP#263 At least one ending edge is straight All ending edges are curved
BP#264 Closed area No closed area
BP#265 Axis of symmetry No axis of symmetry
BP#266 At least one touch or cross point No touch or cross point
BP#267 Odd number of straight line segments Even number of straight line segments
BP#268 Convex hull elongated vertically Convex hull elongated horizontally
BP#269 Center of symmetry No center of symmetry
BP#270 Only vertical or horizontal lines Neither vertical nor horizontal lines
BP#271 Can be hand-written without raising the pen Cannot be hand-written without raising the pen
BP#272 Convex hull is a triangle Convex hull is a quadrilateral
BP#273 Stays put Tumbles
BP#274 Notch from above (holds poured water) No notch from above (does not hold poured water)
BP#275 Straight line joining the ends does not intersect the object Straight line joining the ends intersects the object
BP#276 At least one endpoint No endpoints
BP#277 One object Two or more objects
BP#278 Shorter on the left, taller on the right Taller on the left, shorter on the right
BP#279 The left part has more pixels than the right part The left part has fewer pixels than the right part
BP#280 The left part is wider than the right part The left part is narrower than the right part
BP#281 Equal number of horizontal and vertical lines Unequal number of horizontal and vertical lines
BP#282 Shape of black region same as overall shape of object Shape of black region different from overall shape of object
BP#283 Rectangle left after tiling all black shapes into empty square Triangle left after tiling all black shapes into empty square
BP#284 Half of the square is filled Either more or less than half of the square is filled
BP#285 The centers (“barycenters”) of the objects are collinear The centers (“barycenters”) of the objects are not collinear
BP#286 Decreasing in size from top to bottom Increasing in size from top to bottom
BP#287 “Rays” emanating from a central point
alternative lower-level expression of the same idea:
Altitudes of isosceles triangles meet at a point if extended from top to base		 Not so
BP#288 The sum of the ratios of the filled areas is 1 The sum of the ratios of the filled areas is other than 1
BP#289 Shapes, if tiled up properly, form a square Shapes cannot form a square no matter how they are tiled
BP#290 If any non-nosed faces exist, they are happy if and only if happy nosed faces exist as well Not so
BP#291 The shapes in the large square never appear outside of it At least one shape in the large square appears outside of it
BP#292 Angle made by shapes with vertex at square is not acute Angle made by shapes with vertex at square is acute
BP#293 Square divided into four areas of the same size and shape Not so
BP#294 The two points are reachable through a path The two points are unreachable by any path
BP#295 Line joins large and small square Line joins the two middle-sized squares
BP#296 All three sizes are present Only two of the three sizes present
BP#297 “Ghost shape” is square “Ghost shape” is rectangular
BP#298 One of the two small squares is near the lower-right corner One of the two small squares is near the upper-right corner
BP#299 Lines if slightly extended make up a regular polygon Lines if slightly extended cannot make up a regular polygon
BP#300 Acceleration and deceleration Constant speed
BP#301 Large and medium-sized square, the latter can be hidden Large and small-sized square, the latter can be hidden
BP#302 Collinear objects, of which the 3rd is moved elsewhere Collinear objects, of which the 2nd/4th is moved elsewhere
BP#303 Three objects are identical, the fourth differs Not so
BP#304 At least one (interior or exterior) right angle No right angle (either interior or exterior)
BP#305 Shapes identical after rotation Shapes identical after rotation and mirroring
BP#306 Ratio of inside to outside identical shapes is constant Not so
BP#307 Barycenter of each cluster of dots near a vertex
alternative:
Three or more small clusters of dots		 Not so
BP#308 Three or more small clusters of dots Not so
BP#309 Ball touches curve at a point of local minimum downwards Ball touches curve at a point of local maximum upwards
BP#310 Enclosed square “repelled” by the outside squares, closest to the side of the enclosing square that’s farthest from the common center of the outside squares. Enclosed square “attracted” by the outside squares, closest to the side of the enclosing square that’s closest to the common center of the outside squares.
BP#311 Number of sides – number of pluses = 3 Number of sides – number of pluses = 4
BP#312 Lines intersect within the box Lines intersect out of the box
BP#313 Closed curves clockwise, open curves counterclockwise Closed curves counterclockwise, open curves clockwise
BP#314 Long distance between the marked locations Short distance between the marked locations
BP#315 One area unreachable by the marked locations All areas reachable by the marked locations
BP#316 At least one path is a cycle No path is a cycle
BP#317 Number of enclosed dots proportional to the circle size Not so
BP#318 The numbers of dots are in sequence Not so
BP#319 The number of dots in one cluster is a multiple of the other Not so
BP#320 The numbers of dots in the two clusters are approximately equal The numbers of dots in the two clusters differ a lot
 
BP#321 Small round object unreachable from the border of the box Small round object reachable from the border of the box
BP#322 One outer outline More than one outer outline
BP#323 Jigsaw puzzle pieces can be assembled into a square Jigsaw puzzle pieces cannot be assembled into a square
BP#324 Left shapes can be placed on top of each other to make right shape Not so
BP#325 Left shapes can combine by symmetric difference (“xor” logical operator) to make right shape Left shapes can combine by intersection (“and” logical operator) to make right shape
BP#326 Straight line tangent to circle Straight line not tangent to circle
BP#327 Straight line tangent to curve Straight line not tangent to curve
BP#328 All sides are equal All angles are equal
BP#329 Regular polygon Not regular polygon
BP#330 1-D (line drawing, locally straight line) 2-D
BP#331 2-D (surface, locally flat) 3-D
BP#332 Transparent solid Opaque solid
BP#333 Platonic solid (regular polyhedron) Not a platonic solid
BP#334 Odd number of dots Even number of dots
BP#335 Tessellates the plane Does not tessellate the plane
BP#336 One gear turns all No gear turns all
BP#337 Black is below upward slopes Black is below downward slopes
BP#338 High approximate similarity Low approximate similarity
BP#339 Union of left sets is right set Intersection of left sets is right set
BP#340 Regular star polygons that can be traced vertex-to-vertex in a continuous fashion Not so
BP#341 Strictly increasing or strictly decreasing border line Both increasing and decreasing border line
BP#342 Exactly one axis of symmetry Either zero or more than one axis of symmetry
BP#343 No two shapes are the same At least two shapes are the same
BP#344 Shape can tile with itself so as to create a parallelogram Shape cannot tile with itself so as to create a parallelogram
BP#345 Intersection of circle and square Union of circle and square
BP#346 Object on the right fits in category on the left Object on the right does not fit in category on the left
BP#347 No pattern (variety of shapes) All shapes have something in common
BP#348 Shape on the right is the convex hull of shape on the left Not so
BP#349 One object does not belong to the category of the rest All objects form one category
BP#350 Some quantity keeps increasing from left to right Not so
BP#351 Discrete quantity Continuous quantity
BP#352 Quantity has no lower bound Quantity has lower bound
BP#353 Increasing quantity may loop back to starting value Increasing quantity cannot loop back to starting value
BP#354 Angular quantity Infinitely increasing quantity
BP#355 Fractal iteration based on 2-D (shapes) Fractal iteration based on 1-D (lines)
BP#356 Object at lower-right fits as n-th item in the top row of objects, where n is the number of dots at lower-left Not so
BP#357 Decelerating change in quantity, left-to-right Accelerating change in quantity, left-to-right
BP#358 The circles will collide if the arrows are their velocities The circles will not collide if the arrows are their velocities
BP#359 Random arrangement of dots Non-random (patterned) arrangement of dots
BP#360 Order is high (low entropy) Order is low (high entropy)
BP#361 Analogy makes sense Analogy does not make sense
BP#362 Choice that solves the analogy exists Choice that solves the analogy does not exist
BP#363 Counterclockwise along the curve following the arrow Clockwise along the curve following the arrow
BP#364 Two clearly separable groups No clearly separable groups
BP#365 Two independent quantities changing simultaneously A single quantity is changing
BP#366 White dot is at center of mass White dot is not at center of mass
BP#367 Center of mass within the black area of the shape Center of mass out of the black area of the shape
BP#368 There is a point that can “see” (in straight lines) all points There is no point that can “see” (in straight lines) all points
BP#369 Pairs of points (small white circles) on one curve can be glued together to make the other curve Not so
BP#370 Gluing sides with the same symbols makes a sphere Gluing sides with the same symbols makes a torus
BP#371 Net (folding along edges can make a 3D solid) No net
BP#372 Object belongs to the left-hand side category Object belongs to the right-hand side category
BP#373 Intersection (logical conjunction) Union (logical disjunction)
BP#374 Simple object Complex object
BP#375 Representationally uniform Representationally non-uniform
BP#376 A “chess” piece moving as shown may reach every square Not so
BP#377 The two objects have similar representations The two objects have dissimilar representations
BP#378 The two objects are conceptually related The two objects are conceptually unrelated
BP#379 Complete set Incomplete set
BP#380 The set indicated by the objects is finite The set indicated by the objects is infinite
BP#381 Adding the top two waves yields the bottom wave Not so
BP#382 No knot (“unknot”) Knot
BP#383 When the shape is removed from the dots, the dots give enough information to place the shape back where it was Not so
BP#384 Square number of dots Not a square number of dots
BP#385 Nets of cubes No nets of cubes
BP#386 Lower shape can be used as a tile to build the upper one Not so
BP#387 Dots can be shared equally between figures Dots cannot be shared equally between figures
BP#388 White dot can “see” (in straight lines) all black points White dot cannot “see” (in straight lines) all black points
BP#389 Loops are “entangled” (in 3-D) Loops can be separated (in 3-D)
BP#390 Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) The graph admits nontrivial automorphisms
BP#391 There exists en edge such that removing it yields two disconnected graphs (i.e., the minimum number of edges whose removal results in two disconnected graphs is 1) The minimum number of edges whose removal results in two disconnected graphs is 2
BP#392 Exponential increase Linear increase
BP#393 Correct Incorrect
BP#394 For each colored square only, there exists a path starting on it that covers each square of the figure exactly once There is no path that starts on a colored square and covers each square of the figure exactly once

 

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