Solutions of all sub-problems (rule for left side / right side):
1: With a diagonal (from top left) symmetry axis / without that diagonal symmetry axis;
2: arrows on a line denote a clockwise rotation / anticlockwise;
3: with more upside teeth on the left side / more on the right;
4: black bars growing from the left / from the right (a fully black bar could be on both sides);
5: clockwise spirals / anticlockwise spirals;
6: U shaped figures longer on the right / U shapes figures with longer left arms;
- - - -
7: combs with less than 3 upside teeth / with 3 or more upside teeth;
8: objects with one or more symmetry axis / objects with no specular symmetry axis;
9: acute angles / obtuse angles;
10: big filled objects / small filled objects;
11: approximately triangular objects / other figures;
12: open lines / closed lines.

So my solution to Aaron BP 97 is: the sub-problems of the right boxes are reflection-invariant. So they don't need to tell left from right. The sub-problems of the left boxes instead require you to be able to tell left from right.

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Solutions of all sub-problems:
1: objects with an even number of holes / odd number of holes;
2: combs with 2 or less teeth / combs with 3 or more teeth;
3: objects with many sharp points / with few (5 or less) sharp points;
4: filled polygons with one polygonal hole inside that has less sides than the enclosing polygon / filled polygons with inside one polygonal hole that has more sides than the enclosing polygon;
5: objects with 2 holes / objects with 1 hole;
6: 3x3 matrices with less than 5 black squares / 3x3 matrices with 5 or more black squares;
- - - -
7: acute angles / obtuse angles;
8: U shaped figures longer on the right / U shapes figures with longer left legs;
9: short curved lines / long curved lines;
10: large filled objects / small filled objects;
11: mostly white squares / mostly black squares;
12: triangles mostly filled with white / triangles mostly filled with black.

So my solution to Aaron David Fairbanks BP 92 is: in the left boxes the solving rules of the sub-problems are based on a integer quantitative difference. In the right boxes the sub-problem rules are based on a analog-like quantity (we ignore that these Bongard problems are represented with images made of discrete pixels).

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Solutions of all sub-problems:
1: concave objects / stars;
2: concave objects / C shaped objects;
3: generic filled quadrilaterals / filled squares;
4: generic polygons also with intersecting sides / regular star polygons;
5: objects with some holes / convex polygons with 6 holes;
6: generic objects / C shaped objects;
- - - -
7: objects with bilateral symmetry / objects with rotational symmetry;
8: concave objects / regular (convex) filled polygons;
9: empty regular polygons / C shaped objects;
10: non-square rhombuses / rectangles (oblongs and squares);
11: rod with 5 spaces and 2 pegs up / rod with 5 spaces and and 3 pegs up;
12: regular empty polygons / regular filled polygons.

So my solution to Aaron David Fairbanks BP 77 is: in sub-problems of the left boxes the rule that identifies the objects on the right is a specialization (denotes a subset) of the objects on the left. In the right boxes the objects on the right aren't a subset of the objects on the left (so if you want to identify both exactly you need two different rules).

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Still easy enough.

Solution to Aaron David Fairbanks n. 58: like the precedent Bongard problem, in the upper part of every box there are little tables that define one or more boolean functions with one or two arguments, plus a symbol to denote them. The little black squares represent true values. In the boxes on the left the algebraic expression below (with variables) simplifies to the constant true. In the right boxes the expression can't be simplified to a true constant.

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This was quite easy.

Solution to Aaron David Fairbanks n. 57: in the upper part of every box there are little tables that define one or more boolean functions with one or two arguments, plus a symbol to denote them. The little black squares represent true values. In the boxes on the left the expression below simplifies to the constant true.

#bongardproblem #mathpuzzle #puzzle #visualmath