Index of Bongard Problems

This index contains links to all Bongard problems available to the author. If the reader wants to make their own contribution and enrich this collection, please read this link: Design Your Own Bongard Problems, and also this one: Things Not Allowed in Bongard Problems (but with a grain of salt — use your own judgment).

List of problems by incremental number

There is also a number of meta-Bongard Problems (and meta-meta-BP’s) that the author and Joseph Insana, in cooperation, came up with. What is meant by the term “meta-BP” can be understood by looking at problem #200, above. The best description of meta-BP’s on the web can be found under these pages by Joseph Insana. Implemented meta-BP’s exist also in Aaron David Fairbanks’ collection.

Concepts that Appear in Solutions of Bongard Problems

The following can be seen as a “hints” list, in case you don’t want to be given directly the solutions of BP’s (which are here), but only to know what concepts the solution involves. The concepts index also allows designers to find out if a BP already exists that implements the idea they came up with.

Color-coding showing which concept was originally introduced by which designer (listed chronologically):

Bongard Hofstadter Foundalis Insana Shanahan Howells Gunnarsson Gáspár Lewis Fairbanks Collins

Notes:

Those among the concepts listed below that are primitive are marked with this symbol: on the leftmost column. A composite (non-primitive) concept, for example, is “equilateral triangle”, which can be decomposed based on the primitive concepts: “Vertex of two lines that meet”, “Angle”, “Length of lines”, “Sameness based on feature”, and “Number”. Note: some concepts, such as “Equality”, “Zero” (or any specific small number), “Barycenter of object”, and several more, are too ubiquitous to be included in this list. Sometimes a Bongard Problem (BP) is listed next to a concept not because the concept appears directly in the solution of that BP, but because it is used indirectly. If the concept is present (can be seen) in the BP in general, but is not used (directly or indirectly) in the solution, the BP is not listed next to the concept. This list should be useful to both creators of new BP’s and those few programmers who attempt to automate the solution of BP’s (as the author has done in the past). Thus, creators of new BP’s might want to check which already-known BP’s use the concepts (primitive or composite) in their new BP, to see if their BP is unique. Programmers might want to view this list in the spirit of: “My program should be able to handle these concepts, particularly the primitive ones”. Lastly, a third possible category of people who might find this list useful are those who, like the author, are interested not simply in the automation of solving BP’s, but in modeling visual cognition. This list then can be seen as an attempt to answer the question: which concepts are primitive ( ) in 2-D, black-and-white, visual cognition? Since the list has been constructed by many people contributing to it, it can be viewed as the end-product of the indirect and uncoordinated effort of many people who have created BP’s over a period of many years. It is thus very interesting to see if anyone can find some new primitive concept in the future.