Figural Reasoning and Patterns Flashcards

A 3×3 matrix shows shapes gaining one interior line per column (left to right). The top row has: plain circle, circle with 1 diameter, circle with 2 diameters. The middle-left cell is a plain triangle. What is in the middle-right cell?

Answer: A triangle with two interior lines

Each column adds one interior line, so the rightmost column (column 3) has two interior lines regardless of shape.

A square sheet has a circular hole punched in the upper-left quadrant. The sheet is then folded in half vertically (right flap folds over left). Where do the holes appear when the sheet is fully unfolded?

Answer: Both upper-left and upper-right

Folding the right half over the left mirrors the upper-left hole to the upper-right position, so unfolding reveals holes in both upper quadrants.

A paper is folded in half twice (first horizontally, then vertically) and a small square notch is cut from the center-fold corner. How many holes appear when the paper is fully unfolded?

Answer: 4

Two folds create 4 stacked layers, so one cut through all layers produces 4 holes when unfolded.

A sequence of overlapping shapes cycles as follows: Step 1 = circle on top of square; Step 2 = square on top of triangle; Step 3 = triangle on top of circle. What is Step 5?

Answer: Square on top of triangle

The three-step cycle repeats, so Step 5 = Step 2 = square on top of triangle.

A T-shape starts pointing upward and rotates 90° clockwise each step. In which direction does it point after exactly 6 rotations?

Answer: Rightward

6 ÷ 4 = 1 remainder 2, so after 6 rotations the T-shape is in the same position as after 2 rotations: pointing rightward.

A 3×3 matrix uses three fill types: solid black, gray, and white. Each row and each column contains each fill type exactly once. Row 1 is black, gray, white and Row 2 starts with gray. What fill type is in the bottom-left cell?

Answer: White

Column 1 already has black (Row 1) and gray (Row 2), so the bottom-left cell must be white.

A figure shows concentric rings where Figure 1 has 1 ring, Figure 2 has 2 rings, and so on. How many rings does Figure 8 have?

Answer: 8

The number of rings equals the figure number directly, so Figure 8 has 8 rings.