The On-Line Encyclopedia of Bongard Problems

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Opposite (inverse) transformations have been applied to the same specific small square on opposite sides of the dividing line versus not so.

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	COMMENTS	`The original pre-transformed square is the same across all examples, however it is not shown in most examples; what the pre-transformed square looks like must be deduced by the solver.`
	CROSSREFS	`BP1260 is about applying the same transformation to different objects.` `Adjacent-numbered pages: BP834 BP835 BP836 BP837 BP838 * BP840 BP841 BP842 BP843 BP844`
	KEYWORD	`easy, abstract, arbitrary, anticomputer, traditional, rules`
	CONCEPT	`square (info \| search),` `specificity (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

BP917

Reversible transformations vs. non-reversible transformations.

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	COMMENTS	`All examples depict a process that transforms one object into another (two example input-output pairs are provided in every panel). In left-sorted examples, each input corresponds to a unique output, whereas in right-sorted examples, different inputs could potentially lead to the same output. There is a sense in which all the processes described on the right "lose" some amount of the input's information.`
	REFERENCE	`https://en.wikipedia.org/wiki/Injective_function`
	CROSSREFS	`Adjacent-numbered pages: BP912 BP913 BP914 BP915 BP916 * BP918 BP919 BP920 BP921 BP922`
	KEYWORD	`nice, abstract, creativeexamples, structure, rules, miniworlds`
	CONCEPT	`convey_enough_information (info \| search),` `function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP951

Process described leaves some inputs invariant vs. no output will resemble its input.

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	COMMENTS	`There are many ambiguities here. The solver is expected to determine what things are "allowed" to be inputs for each process. To avoid confusion examples should not be sorted differently if you consider inputting nothing.` `In each example there is at least some overlap between the set of possible inputs and the set of possible outputs for each process. If we did not apply this constraint, an easy example to be sorted right would be a process that turns blue shapes red.` `A harder-to-read but more clearly defined version of this Problem could include within each example a mini Bongard Problem sorting left all allowed inputs for the process.`
	REFERENCE	`https://en.wikipedia.org/wiki/Fixed_point_(mathematics)`
	CROSSREFS	`Adjacent-numbered pages: BP946 BP947 BP948 BP949 BP950 * BP952 BP953 BP954 BP955 BP956`
	KEYWORD	`structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1110

The process that turns one object into the other is the same both ways vs. the process changes depending on which object is chosen as the starting point.

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	REFERENCE	`https://en.wikipedia.org/wiki/Duality_(mathematics)` `https://en.wikipedia.org/wiki/Involution_(mathematics)`
	CROSSREFS	`This is a special case of BP841 and a generalisation of BP822.` `Adjacent-numbered pages: BP1105 BP1106 BP1107 BP1108 BP1109 * BP1111 BP1112 BP1113 BP1114 BP1115`
	KEYWORD	`nice, abstract, math, anticomputer, creativeexamples, left-narrow, unorderedpair, rules, miniworlds, dithering`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1157

The order in which the objects in the top half are combined to make the object in the lower half matters vs. not so.

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	COMMENTS	`Operations depicted in right-sorted examples are called "commutative".` `"Order matters" here means that if the objects in the top half were to switch places, the output would look different.`
	REFERENCE	`https://en.wikipedia.org/wiki/Commutative_property`
	CROSSREFS	`Adjacent-numbered pages: BP1152 BP1153 BP1154 BP1155 BP1156 * BP1158 BP1159 BP1160 BP1161 BP1162`
	KEYWORD	`nice, abstract, unwordable, notso, structure, rules, miniworlds`
	CONCEPT	`function (info \| search)`
	AUTHOR	`Leo Crabbe`

BP1260

Same transformation applied to circle, triangle, and square vs. different transformations applied.

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	CROSSREFS	`BP839 is about applying opposite transformations to a single object.` `Adjacent-numbered pages: BP1255 BP1256 BP1257 BP1258 BP1259 * BP1261 BP1262 BP1263 BP1264 BP1265`
	KEYWORD	`easy, nice, abstract, arbitrary, anticomputer, left-null, structure, orderedtriplet, traditional, rules`
	CONCEPT	`circle (info \| search),` `analogy (info \| search),` `square (info \| search),` `same (info \| search),` `triangle (info \| search),` `function (info \| search)`
	AUTHOR	`Aaron David Fairbanks`

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