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`

BP1150

Even BP number on the OEBP vs. odd BP number on the OEBP.

	BP2	BP4	BP6	BP8	BP10	BP12
	BP14	BP16	BP18	BP20	BP100	BP1150

	BP1	BP3	BP5	BP7	BP9	BP11
	BP13	BP15	BP17	BP19	BP1073

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	COMMENTS	`This was created as an example for BP1073 (left-it versus right-it).`
	CROSSREFS	`Adjacent-numbered pages: BP1145 BP1146 BP1147 BP1148 BP1149 * BP1151 BP1152 BP1153 BP1154 BP1155`
	KEYWORD	`less, meta (see left/right), links, oebp, example, left-self, presentationmatters, right-it, experimental, left-listable, right-listable`
	CONCEPT	`even_odd (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.

(edit; present; nest [left/right]; search; history)

	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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