[Math] Pattern-matching puzzle (shapes)

intuitionpuzzle

some puzzle that can be found online are typically a 3×3 grid where you've got nine spots filled with some images or symbols or geometric figures and you have to predict what the missing one should be. Some of them are made out of symbols, some other are little 3×3 grids (inside the big grid) with some number of symbols (crosses, asterisks, etc..) placed according to some pattern and, again, you have to guess what pattern the missing grid would be.

Does anyone have any reference where I can find how they can be solved, or any theory behind this kind of puzzle?

EXAMPLES:

Bergman's IQ test

IQ test

Again, I am not looking to the specific solution of the examples above. I'd like to have a theory behind it, or tips to solve them.

Best Answer

While one might use mathematical thought to invent justifications about what symbol comes next, the major component of this puzzle is human perception. The viewer is the one who decides what features are important, and what things are meaningful.

You can contrast this type of puzzle with something like Sudoku, which really does reduce to a deterministic mathematical study. There isn't (supposed to be) any ambiguity about what comes next in those puzzles.

Pattern recognition is certainly important in mathematics, but actually I think it is more primitive because it relates to our perception and learning process. This indicates that you will get better, more interesting answers about solving such questions if you ask psychologists and/or machine learning experts.

Related Solutions

[Math] Puzzle: numerical pattern recognition

This is all I can come up with:

1: Do the operation, the answer to that will be placed on the far right:

$ \begin{align} 7-3 &= 4 \\ 6 + 3 &=9 \\ 5-2 &= 3 \\ 11 + 2 &= 13 \end{align}$

2: Take the solution from above, multiply by the second digit in the original expression. Place it to the left of the answer we got in 1.:

$ \begin{align} 4\cdot 3 &= 12 \\ 9\cdot 3&=27 \\ 3\cdot 2&= 6 \\ 13 \cdot 2 &= 26 \end{align}$

So, we have

$ \begin{align} 124 \\ 279 \\ 63 \\ 2613 \end{align}$

3: If the original operation was addition, subtract, and vice versa. Stick this number to the left of the concatenated solutions to 1 and 2:

$ \begin{align} 7+3 &= 10 \\ 6 - 3 &=3 \\ 5+2 &= 7 \\ 11 - 2 &= 9 \end{align}$

Thus, we have

$ \begin{align} 10124 \\ 3279 \\ 763 \\ 92613 \end{align}$

[Math] Sudoku with special properties

Proof that $N=49$ is impossible:

+-------+---   1) +-------+      2) +-------+      3) +-------+
| 1 2 3 | X       |(1)2 3 |*1       | 1 2 3 |(7)      | 1 2 3 |(4)
| 4 5 6 | Y       |(4)5 6 |*4       | 4 5 6 | 1       |(4)5 6 | 7
| 7 8 9 | Z       |(7)8 9 |*7       |(7)8 9 | 4       | 7 8 9 | 1
+-------+---      +-------+         +-------+         +-------+ 
| A B C | D       | A B C | D       | A*B*C |*D       | A*B*C |*D

The block on the first figure is to be taken as our "starting" one. Since there are no other numbers on the board, having them ordered makes no difference, for now. Now, there are 3 different ways to fill tiles XYZ with 1 4 and 7, but they all fail. Since:

Case 1: Obviously, there's 3 collisions.

Case 2: BCD must contain 237 on any order. However, 7 can't be on B or C because it collides with our original grid. And it can't be on D either, because it's on the same row as the recently added one.

Case 3: Similar to before, except with 4.

That means there's no way to have those 2 blocks (23X,56Y,89Z and 56Y,89Z,BCD) successfully.

Therefore, $N=49$ is impossible.

Best Answer

Related Solutions

[Math] Puzzle: numerical pattern recognition

[Math] Sudoku with special properties

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