The On-Line Encyclopedia of Bongard Problems

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BP1146

Same number of dots in top row as in leftmost column vs not so.

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	COMMENTS	`This is a difficult-to-read attempt at making a Bongard Problem about perfect numbers. Grouping columns together to make rectangular arrays, each maximal (most dots possible) rectangular array of a particular height in any given example has the same number of dots in it (a perfect number, in left-sorted cases), and the dot-width of each array represents a particular divisor of that number.` `It is not currently known whether there are a finite amount of examples that would be sorted left.` `Every example in this Bongard Problem corresponds to a distinct natural number. There is not a way of representing the number 1 using the rules of construction for examples in this problem (if the problem were simply "Perfect number of dots vs. other number of dots", the example with 1 dot would be sorted right).`
	REFERENCE	`https://en.wikipedia.org/wiki/Perfect_number`
	CROSSREFS	`Adjacent-numbered pages: BP1141 BP1142 BP1143 BP1144 BP1145 * BP1147 BP1148 BP1149 BP1150 BP1151`
	KEYWORD	`overriddensolution, left-listable, right-listable`
	AUTHOR	`Leo Crabbe`

BP1147

Columns of the table could be respectively labeled "Number" and "Number of times number appears in this table" vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1142 BP1143 BP1144 BP1145 BP1146 * BP1148 BP1149 BP1150 BP1151 BP1152`
	KEYWORD	`nice, precise, notso, handed, leftright, left-narrow, grid, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1148

Number of dots in the Nth box (from the left) is how many times the number (N - 1) appears in the whole diagram vs. not so.

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	COMMENTS	`Left-sorted examples are sometimes called autobiographical or self-descriptive numbers.`
	REFERENCE	`https://oeis.org/A349595` `https://en.wikipedia.org/wiki/Self-descriptive_number`
	CROSSREFS	`See BP1147 for a similar idea.` `BP1149 was inspired by this.` `Adjacent-numbered pages: BP1143 BP1144 BP1145 BP1146 BP1147 * BP1149 BP1150 BP1151 BP1152 BP1153`
	KEYWORD	`nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1149

Number in the Nth box (from the left) is how many numbers appear N times vs. not so.

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	CROSSREFS	`Inspired by BP1148.` `Adjacent-numbered pages: BP1144 BP1145 BP1146 BP1147 BP1148 * BP1150 BP1151 BP1152 BP1153 BP1154`
	KEYWORD	`nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable`
	CONCEPT	`self-reference (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1197

No sequence is repeated twice in a row vs. some sequence is repeated twice in a row.

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	REFERENCE	`https://en.wikipedia.org/wiki/Square-free_word`
	CROSSREFS	`Adjacent-numbered pages: BP1192 BP1193 BP1194 BP1195 BP1196 * BP1198 BP1199 BP1200 BP1201 BP1202`
	KEYWORD	`precise, allsorted, notso, left-narrow, sequence, traditional, preciseworld, dithering, left-listable`
	CONCEPT	`two (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP1199

The only rectangles are the individual regions and the whole vs. there is some other rectangle made of rectangles.

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CROSSREFS

All of the examples fitting left here would fit right in BP1200 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.

All of the examples fitting left in BP1097 (re-styled) would fit right here (besides the two possible arrangements made up of just two rectangles, but those aren't shown there).

See BP1201 for the version with triangles.

Adjacent-numbered pages: BP1194 BP1195 BP1196 BP1197 BP1198 * BP1200 BP1201 BP1202 BP1203 BP1204

KEYWORD

precise, traditional, left-listable, right-listable

AUTHOR

Aaron David Fairbanks

BP1200

The whole rectangle can be filled in by successively replacing pairs of adjacent rectangles with one vs. not so.

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	COMMENTS	`Another wording: "can be repeatedly broken along 'fault lines' to yield individual pieces vs not."`
	REFERENCE	`Robert Dawson, A forbidden suborder characterization of binarily composable diagrams in double categories, Theory and Applications of Categories, Vol. 1, No. 7, p. 146-145, 1995.`
	CROSSREFS	`All of the examples fitting left here would fit right in BP1199 except for (1) a single rectangle, (2) two rectangles stacked vertically, or (3) two rectangles side by side horizontally.` `All of the examples fitting right in in BP1097 (re-styled) would fit right here (besides a single solid block, but that isn't shown there).` `Adjacent-numbered pages: BP1195 BP1196 BP1197 BP1198 BP1199 * BP1201 BP1202 BP1203 BP1204 BP1205`
	KEYWORD	`hard, precise, challenge, proofsrequired, inductivedefinition, left-listable, right-listable`
	AUTHOR	`Aaron David Fairbanks`

BP1201

The only triangles are the individual regions and the whole vs. there is some other triangle made of triangles.

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	CROSSREFS	`See BP1199 for the version with rectangles.` `Adjacent-numbered pages: BP1196 BP1197 BP1198 BP1199 BP1200 * BP1202 BP1203 BP1204 BP1205 BP1206`
	KEYWORD	`precise, traditional, left-listable, right-listable`
	CONCEPT	`triangle (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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