Which of the 8 tiles below is missing?
I've been trying to figure out the answer to this question for quite some time. Can anyone spot the pattern?
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I think the answer is
Because it looks to me like
Reading from left to right, the lines continue where the previous square left off, to make two long connecting 'strings' of sorts. The eighth square leaves off in the top righthand corner and about 80% of the way down the bottom side, which is where tile 5 would connect to.
Here is an image of the final solution:
I think the answer is
The one given by @Bailey M, but I would like to offer another answer...
Because I figured that
It would be fun to have an alternative solution :-). With this solution, the supposed rules for tiles are that:
1. the third column tiles' lines always "indicate" adjoined sides;
2. the third column tiles' lines always touch exactly one corner;
Tiles 1, 2, 7, and 8 are out because of rule 1;
Tiles 4, 5, 6, (and 7) are out because of rule 2;
And thus that
it must be Tile 3!
Here's an image to visualize that
I think Bailey M has got the intended answer.
But another answer that works is
In each square, label the corners A-D, running clockwise from the top left. By "line" we mean a line inside a square. Call a line "par" if it is parallel to a side of the square. Call a corner "visited" if it is touched by a line.
Consider the distribution of par lines by row. In rows 1-2 the totals are the same: each row contains exactly 1. To continue the pattern of sameness, row 3 must also contain exactly 1. Of all the possible missing tiles, the only one that contains exactly 1 par line is tile 2.
Second and corroborating fact.
Now consider the distribution of par lines by column. In columns 1-2 the numbers are different: there are 0 in column 1 and 2 in column 2. Neither of the known tiles in column 3 contains a par line, so the total in column 3 can only be 0 or 1. To continue the pattern of difference, the number must be 1, so again the answer must be tile 2.
Third and supporting fact
Each fully known column contains exactly 2 squares in which the same corner is visited: in column 1, that is corner B; in column 2, corner C. So we need a tile that continues that pattern in column 3. The visited corners in the known tiles in column 3 are A and C. This restricts the possibilities for the missing tile to tiles 2 and 5. So when we choose tile 2, this pattern also continues.
Diagram of this solution:
Of course this answer doesn't use all of the given information. For example, the horizontal line in the top middle tile could be translated upwards and everything would still apply. But the same is true of what appears to be the intended solution. In that solution, it doesn't matter whether two lines in a square cross or don't cross, so long as they start and end so as to connect with the lines in adjacent squares. One could also say that going downwards for row 2 but left-to-right for rows 1 and 3 is a bit arbitrary. Our basis for deciding what we think is the best solution is subjective, or at least would take a lot of definition to be made objective.
I think the answer should be
(3) because for every figure you see in a row one end of two lines lies on one side and other end on another side and also 2 out of 3 of such figures have such sides opposite to each other and one has it adjacent (note having line start at edge should be interpreted as in a favor of this hypothesis i.e. benefit of doubt goes to me). Same pattern is seen in row 2 and hence extrapolating it, I eliminate the eight-options to arrive at (3) which satisfies this rule.