The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Note that all examples shown in this Bongard Problem result from collapsing a subdivided rectangle (such that all vertical lines are shrunken to points). Examples shown on the right of this Bongard Problem are examples that would fit left, but further collapsed: some 2D regions have been collapsed down into horizontal line segments.

Here is another answer:

"Right examples: some loop is adjacent to a flat line segment, and the two are not separated by a taller containing loop."

And this was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

Here are some subtleties to this string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

BP1129 started as an incorrect solution for this Bongard Problem. Anything fitting right in BP1130 fits right in BP1129.

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are like examples that would fit left, but some regions are further collapsed into horizontal lines

Here is another answer:

"Right examples: some loop is adjacent to a flat line segment, and the two are not separated by a taller containing loop."

And this was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

Here are some subtleties to this string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are like examples that would fit left, but some regions are further collapsed into horizontal lines

Here is another answer:

"Right examples: some loop is next to a flat line segment, and the two are not separated by a taller containing loop."

And this was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

Here are some subtleties to this string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are just like examples that would fit left except some regions are further collapsed into horizontal lines

Here is another answer:

"Right examples: some loop is next to a flat line segment, and the two are not separated by a taller containing loop."

And this was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

Here are some subtleties to this string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are just like examples that would fit left except some regions are further collapsed into horizontal lines

Thus here is another answer:

"Right examples: some loop is next to a flat line segment, and the two are not separated by a taller containing loop."

And this was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

Here are some subtleties to this string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

This was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

Here are some subtleties to this string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

This was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind.

Here are some subtleties to the string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

This was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind.

Here are some subtleties to the string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the other regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

This was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind.

Here are some subtleties to the string sweeping rule. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string through an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

This was the original, more vague description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is harder to make this intuition precise.

Here are some subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is harder to make this intuition precise.

Here are some subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Some subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a segment of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no segment of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string can stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that shape. In particular, shrinking vertical lines of a rectangle into points means just those points of the string ever stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

It seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as defining an animation of a string sweeping across that shape. In particular, shrinking vertical lines of the rectangle into points means just those points of the string ever stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

The answer seems quite convoluted spelled out in detail, at least like this. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as defining an animation of a string sweeping across that shape. In particular, shrinking vertical lines of the rectangle into points means just those points of the string ever stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

This answer seems quite convoluted spelled out like this in detail. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as defining an animation of a string sweeping across that shape. In particular, shrinking vertical lines of the rectangle into points means just those points of the string ever stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some squashed-down version of a subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

This answer seems quite convoluted spelled out like this in detail. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as defining an animation of a string sweeping across that shape. In particular, shrinking vertical lines of the rectangle into points means just those points of the string ever stay still as the string sweeps down.

Note that all examples shown in this Bongard Problem are some form of squashed-down subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

This answer seems quite convoluted spelled out like this in detail. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as defining an animation of a string sweeping across that shape. In particular, shrinking vertical lines of the rectangle into points means just those points of the string keep stationary for some time while the string sweeps down.

Actually, all examples shown in this Bongard Problem are some form of squashed-down subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).

The rectangle-based description was noted by Sridhar Ramesh when he solved this.

Here is the original, more vague and instinctive description:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. Only in left images can this be done so that no portion of the string ever hesitates."

If a person who is trying to solve this Bongard Problem says something along these lines, they likely have the correct answer in mind. It is not so easy to make this intuition precise.

Here are the subtleties to this idea worth mentioning. Each point on the string can only move vertically. The string may only enter a region when the string fully covers that region's top edge (and likewise it must exit by fully covering the bottom edge). Thus a portion of string cannot enter a region until the string is finished sweeping down all the regions directly above.

This answer seems quite convoluted spelled out like this in detail. (Although it is not terribly complicated imagined visually. See the keyword "unwordable" left-BP506.)

The string-sweeping answer is equivalent to the rectangle answer because a rectangle indexes the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as defining an animation of a string sweeping across that shape. In particular, shrinking vertical lines of the rectangle into points means just those points of the string keep stationary for some time while the string sweeps down.

Actually, all examples shown in this Bongard Problem are some form of squashed-down subdivided rectangle. The examples shown on the right of this Bongard Problem are examples that would fit left but with some whole ovals collapsed into just horizontal lines (leaving a length of string stationary in the animation).