The On-Line Encyclopedia of Bongard Problems

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At least twice as many of one color than the other vs. neither color attains double the other.

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	CROSSREFS	`See the twin BP1052.` `Adjacent-numbered pages: BP1042 BP1043 BP1044 BP1045 BP1046 * BP1048 BP1049 BP1050 BP1051 BP1052`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`ratio (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Two parts black to one part white vs. not so.

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	CROSSREFS	`See the twin BP1047.` `Adjacent-numbered pages: BP1048 BP1049 BP1050 BP1051 BP1052 * BP1054 BP1055 BP1056 BP1057 BP1058`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`ratio (info \| search),` `one (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Ratio of total circles to black circles is a power of two vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1049 BP1050 BP1051 BP1052 BP1053 * BP1055 BP1056 BP1057 BP1058 BP1059`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`ratio (info \| search),` `two (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Top layer is two vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1053 BP1054 BP1055 BP1056 BP1057 * BP1059 BP1060 BP1061 BP1062 BP1063`
	KEYWORD	`arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `specificity (info \| search),` `two (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Specific structure vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1058 BP1059 BP1060 BP1061 BP1062 * BP1064 BP1065 BP1066 BP1067 BP1068`
	KEYWORD	`notso, arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `specificity (info \| search),` `one (info \| search),` `two (info \| search),` `three (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Every nonempty region has two boxes vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1063 BP1064 BP1065 BP1066 BP1067 * BP1069 BP1070 BP1071 BP1072 BP1073`
	KEYWORD	`arbitrary, perfect, infinitedetail`
	CONCEPT	`fractal (info \| search),` `recursion (info \| search),` `self-reference (info \| search),` `two (info \| search)`
	WORLD	`recursive_boxes [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

Each attribute is shared by every group or none vs. some attribute is shared by exactly two groups

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	COMMENTS	`Attributes are shading, shape, and number.` `There are always three groups.` `This problem is related to the card game Set.`
	CROSSREFS	`Adjacent-numbered pages: BP1133 BP1134 BP1135 BP1136 BP1137 * BP1139 BP1140 BP1141 BP1142 BP1143`
	KEYWORD	`nice, precise, allsorted, notso, preciseworld`
	CONCEPT	`all (info \| search),` `number (info \| search),` `same (info \| search),` `two (info \| search),` `three (info \| search)`
	AUTHOR	`William B Holland`

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`

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