The On-Line Encyclopedia of Bongard Problems

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Reciprocals of right numbers summed in infinite series converge vs. diverge.

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	CROSSREFS	`Adjacent-numbered pages: BP1033 BP1034 BP1035 BP1036 BP1037 * BP1039 BP1040 BP1041 BP1042 BP1043`
	KEYWORD	`hard, precise, allsorted, handed, leftright, math, challenge, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1039

"Greater than ___ vs. less than ___" vs. other solution.

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	CROSSREFS	`See the twin BP1031.` `Adjacent-numbered pages: BP1034 BP1035 BP1036 BP1037 BP1038 * BP1040 BP1041 BP1042 BP1043 BP1044`
	KEYWORD	`precise, allsorted, notso, handed, leftright, math, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1040

Left is union of (non-constant) arithmetic progressions vs. not so.

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	CROSSREFS	`Adjacent-numbered pages: BP1035 BP1036 BP1037 BP1038 BP1039 * BP1041 BP1042 BP1043 BP1044 BP1045`
	KEYWORD	`hard, precise, allsorted, convoluted, notso, handed, leftright, math, challenge, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1041

Right finite vs. right infinite.

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	CROSSREFS	`See BP1032 for left infinite vs. left finite. That is this Problem with with sides flipped and sides of mini-Problems flipped.` `See BP516 (right-finite) for a version that sorts links to Bongard Problems and not just about numbers, instead of images of Bongard Problems (miniproblems) about numbers.` `Adjacent-numbered pages: BP1036 BP1037 BP1038 BP1039 BP1040 * BP1042 BP1043 BP1044 BP1045 BP1046`
	KEYWORD	`precise, allsorted, handed, leftright, meta (see left/right), miniproblems, assumesfamiliarity, structure, preciseworld`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1042

"No panels vs. dots" or "dots vs. no panels" vs. other dots Bongard Problem.

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	CROSSREFS	`Adjacent-numbered pages: BP1037 BP1038 BP1039 BP1040 BP1041 * BP1043 BP1044 BP1045 BP1046 BP1047`
	KEYWORD	`less, precise, allsorted, notso, meta (see left/right), miniproblems, example, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	CONCEPT	`or (info \| search)`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1043

Dots Bongard Problem vs. nothing.

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	CROSSREFS	`Adjacent-numbered pages: BP1038 BP1039 BP1040 BP1041 BP1042 * BP1044 BP1045 BP1046 BP1047 BP1048`
	KEYWORD	`less, precise, allsorted, notso, meta (see left/right), miniproblems, example, assumesfamiliarity, structure, preciseworld, presentationinvariant`
	WORLD	`boxes_dots_bpimage_clear_set_of_numbers [smaller \| same \| bigger] zoom in right (nothing)`
	AUTHOR	`Aaron David Fairbanks`

BP1044

More black circles than white circles vs. at least as many white circles as black circles.

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	CROSSREFS	`See the twin BP1046.` `Adjacent-numbered pages: BP1039 BP1040 BP1041 BP1042 BP1043 * BP1045 BP1046 BP1047 BP1048 BP1049`
	KEYWORD	`precise, allsorted, spectrum, discrete, preciseworld`
	CONCEPT	`ratio (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1045

More of some color vs. half and half.

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	CROSSREFS	`Adjacent-numbered pages: BP1040 BP1041 BP1042 BP1043 BP1044 * BP1046 BP1047 BP1048 BP1049 BP1050`
	KEYWORD	`precise, allsorted, preciseworld`
	CONCEPT	`ratio (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1046

More white circles than black circles vs. at least as many black circles as white circles.

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

	CROSSREFS	`See the twin BP1044.` `Adjacent-numbered pages: BP1041 BP1042 BP1043 BP1044 BP1045 * BP1047 BP1048 BP1049 BP1050 BP1051`
	KEYWORD	`precise, allsorted, spectrum, discrete, preciseworld`
	CONCEPT	`ratio (info \| search)`
	WORLD	`outline_or_fill_circles_same_size [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP1047

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

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

	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`

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