The Arrow That Keeps Turning
A sequence of five frames runs left to right with the fifth frame blank. Each frame holds one arrow and a single horizontal row of small dots beneath it.
Frame 1: arrow points straight up, filled solid black; one dot. Frame 2: arrow points up and to the right (45° clockwise from frame 1), white with a black outline; two dots. Frame 3: arrow points right, solid black; three dots. Frame 4: arrow points down and to the right, white with a black outline; four dots.
Across the four frames the arrow keeps the same length and shaft, the dots keep the same size and spacing, and the arrow is only ever turned - never flipped. No frame contains more than one arrow, and no frame adds or removes any element other than the dots.
Five options are offered for frame 5, varying in arrow direction, arrow fill and dot count.
1. Describe frame 5 completely and justify each attribute separately.
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Treat the three attributes as three independent rules and check each one on its own:
- Direction: 45° clockwise per frame - up, up-right, right, down-right - so frame 5 points straight down.
- Fill: black, white, black, white, so frame 5 is solid black.
- Dots: one more each frame - 1, 2, 3, 4 - so frame 5 has five evenly spaced dots in a horizontal row.
Answer: a solid black arrow pointing straight down with five dots beneath it.
Before committing, scan the options for near-misses: a down-right arrow (one step behind), a white down arrow (fill rule dropped), a black down arrow with four dots (dot rule dropped). Each wrong option should fail exactly one rule. If an option fails none, the item has two correct answers and needs rebuilding.
2. A student answers 'arrow pointing up, black, one dot, because the pattern starts again after four steps.' Identify the error and the evidence in frames 1-4 that rules it out.
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The error is noticing that direction appears to repeat and assuming the whole figure restarts. Two things are wrong with that.
First, the arithmetic: 45° × 4 = 180°, not 360°, so the arrow has not returned to 'up' at frame 5 - it is pointing down.
Second, the other attributes show no repetition at all. The dots run 1, 2, 3, 4 with no return, and the fill alternates without resetting. A genuine restart would require frame 5 to match frame 1 in every attribute simultaneously; nothing in frames 1-4 supports that.
The student has let one attribute's near-cycle override the evidence from the other two. The reliable habit is to tabulate each attribute in its own row before combining them, so a cycle in one row cannot masquerade as a cycle in the pattern.
3. Predict frame 8. Then say which attribute is the first to look ambiguous as the sequence runs on, and why.
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Frame 8: seven 45° clockwise steps from up is 315°, so the arrow points up and to the left; the fill is white (frames 5, 6, 7, 8 run black, white, black, white); the dot count is eight.
Direction is the first attribute to look ambiguous, because it is the only one that returns to a previously seen value. At frame 9 the arrow points up again (360°), and the fill is black again too - both attributes now match frame 1 exactly. Only the dot count, nine against one, shows that the sequence has not restarted. A student who is pattern-matching rather than tracking will read frame 9 as 'frame 1 again' and predict a reset.
The rule itself never becomes ambiguous; the visual recycling does the damage. The dot count is the safest anchor in a long sequence because it never repeats a value.