# A Layered Problem

This is my own work.

If you would like to see examples of similar problems, to help you understand what to do please see my other posts. (e.g. What's the question to this and what is its answer?) • I thought I had it, but the large square immediately left of the vertical line's center spoils my answer. – aschepler Nov 16 '19 at 2:22
• @aschepler thanks for pointing this out. i have corrected the problem now. – JAGO Nov 16 '19 at 10:47

The overall question is:

Does the puzzle on the bottom fit with the group of five puzzles on the left or the group of five puzzles on the right?

The bottom puzzle fits with the left group, because it has two reasonable answers.

Reasoning:

First, label the eleven large squares:

A B | F G
C D | H J
E   |   K

L


Each of those eleven large squares represents a puzzle in which the task is to determine whether its bottom square fits with a common property of its left group of five sample squares above, or with its right group of five.

For the left five puzzles A-E, both answers are reasonably valid for different reasons:

A: The bottom tile belongs with the left group because it has a diamond, not a star. Or, the bottom tile belongs with the right group because it has a solid black shape, not an outlined white shape.

B: The bottom tile belongs with the left group because it has a black shape on a white background, not white on black. Or, the bottom tile belongs with the right group because it does not have vertical symmetry.

C: The bottom tile belongs with the left group because it has two line segments, not three. Or, the bottom tile belongs with the right group because its line segments are not parallel.

D: The bottom tile belongs with the left group because its square's edges are horizontal and vertical, not at 45-degree angles to the main grid. Or, the bottom tile belongs with the right group because it has two dots, not one.

E: The bottom tile belongs with the left group because its dots are grouped into two clusters, not one cluster. Or, the bottom tile belongs with the right group because it has an odd number of dots, not even.

The right five puzzles F-K each have one correct answer:

F: The bottom tile belongs with the left group of solid black circles.

G: The bottom tile belongs with the right group, where each has two black circles and one white triangle, not the left's one black circle and two white triangles.

H: The bottom tile belongs with the right group, since it has a black round shape, and does not have the white triangle shape common to the left group.

J: The bottom tile belongs with the right group, since it has a white triangle on black, not a black circle on white.

K: I'll get back to K.

So that leaves puzzle L, which has two reasonable answers: The bottom tile belongs with the left group because it has a solid black shape, not an outlined white shape. Or, the bottom tile belongs with the right group because it has a triangle, not a circle.

So looking at the bigger metapuzzle, puzzle L belongs to the left group of puzzles with double answers, assuming K has exactly one correct answer.

K: The bottom tile belongs to the left group, because each tile represents one of the puzzles in the metapuzzle, and the bottom tile represents a puzzle with multiple solutions, not a puzzle with one solution. (A near hit for K is that each of its left tiles clearly belongs to one of the two groups in that tile's corresponding puzzle, and each of its right tiles could be seen as belonging to either group in that tile's corresponding puzzle - but the tile for puzzle G breaks the pattern, clearly belonging to the right group within puzzle G. So this interpretation isn't a valid second answer to K.)

Yes, this is circular reasoning. But if K doesn't have exactly one valid solution, then most likely the metapuzzle doesn't have any reasonable solution, unless it's something entirely different from these ideas. Since our task is to find solutions, better go with the consistent possibility.