The Pattern Grid
You are shown a 3x3 grid of symbols. Row 1: a solid circle, a solid circle with one vertical line through it, a solid circle with two vertical lines. Row 2: a solid square, a solid square with one horizontal line, a solid square with two horizontal lines. Row 3: a solid triangle, a solid triangle with one diagonal line, and a blank cell. You must choose the missing symbol from four options: (A) triangle with two diagonal lines, (B) triangle with one vertical line, (C) circle with two diagonal lines, (D) triangle with two horizontal lines.
1. Describe the rule governing each row and column, and select the correct option.
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Row rule: the base shape is constant within a row (row 1 circles, row 2 squares, row 3 triangles). The number of overlaid lines increases left to right: 0, 1, 2.
Column rule: the number of lines is constant within a column (column 1 = 0 lines, column 2 = 1 line, column 3 = 2 lines). The orientation of the lines follows the row: vertical for row 1, horizontal for row 2, diagonal for row 3.
Missing cell: row 3, column 3 → triangle with two lines, oriented diagonally (matching the row's line orientation).
Answer: (A).
Reasoning: (B) has the wrong number and orientation; (C) has the wrong base shape; (D) has the wrong orientation. Only (A) satisfies both the row and column rules simultaneously.
2. A colleague claims the answer could be (D) if the rule is 'lines rotate 90 degrees down each column'. Test this claim.
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Test the column-rotation rule: if lines rotate 90 degrees down each column, then column 2 would be vertical (row 1), horizontal (row 2), vertical (row 3) - but the given row 3 cell in column 2 is a triangle with a diagonal line. So the rotation rule is contradicted by the data.
Test (D) directly: (D) is a triangle with two horizontal lines. Under the row rule, row 3's line orientation is diagonal, not horizontal. Under the column rule, column 3 requires two lines - which (D) has - but the orientation is wrong.
Conclusion: (D) fails the row rule. The colleague's alternative rule does not fit the given cells, so it must be rejected. The correct answer remains (A).
Reasoning principle: a proposed rule must explain all given cells, not just the ones convenient to the hypothesis. A rule that contradicts even one known cell is invalid.