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The full answer is 11 letters long.
Hint1
You have to solve the top rebus first. After you've solved it, you'll hopefully realize, with (or without) the help of the knowledge-tag, what the problem is.
Hint2(Rebus)
What animal is it?
Final answer
Esther Klein, the mathematician who came up with the problem referenced in this puzzle.
Part 1, rebus
Inside the face we have the atomic number of Nitrogen, a Dingo and a picture of Nitrogen dioxide, i.e., NO2. These give
N + DINGO + NOO = N + DINGO + (No O) = EN + DINGO - O = ENDING
All of this is inside a happy face, so in total it gives
HAPPY ENDING
Part 2, the problem
The happy ending problem is a mathematical problem that says that for any positive integer N, there exists a large enough number M, s.t., if we place M points on a plane such that no three points are collinear, then there must be a subset of N points which form the vertices of a convex N-gon.
In particular, it was first proven that any five points must contain a convex quadrilateral. In that case, there are three different cases to consider pictured here
In the first case, all five points form a convex 5-gon, in which case any four points will form a convex quadrilateral so there are five ways to form the quadrilateral.
In the second case the convex hull is a quadrilateral with one point inside it. In this case either the corners of the convex hull can form a quadrilateral or we can draw a diagonal and leave out the corner point which ends up on the same side as the point in the middle. Thus, in this case, there are three ways to form the quadrilateral.
In the third case the convex hull is a triangle. In this case there is only one way to form the quadrilateral: with the two points inside and with the two points that would end up on the same side of the line extended from the two interior points.
The grids in the puzzle are all of the first or second type. The quadrilaterals can be formed in
5, 3, 5, 3, 5, 3
ways.
Part 3, extraction
The rebus here says
DIG + IT = DIGIT
indicating that we should take digits from the previous step and map them to the corresponding letter grids. OP commented that there is a small mistake in the puzzle so that the 5s of previous step are actually in position 4. Note also that the letter grids start at zero. Taking the correct letters gives
E KLEIN,
i.e., Esther Klein, who introduced this problem to Paul Erdős and George Szekeres.
