Veritasium: The SAT Question Everyone Got Wrong [video]
An SAT math problem from 1982 about a small circle rolling around a larger one has resurfaced after a Veritasium video argued the official answer was wrong, highlighting how ambiguous wording can hide multiple mathematically valid interpretations. Commenters explore intuitive ways to understand why the “coin around coin” setup yields an extra rotation, connect it to concepts like sidereal time and planetary motion, and reference related competition problems and resources. The thread broadens into a critique of standardized testing, vague problem design, and how much exams measure true reasoning versus familiarity with test-writers’ assumptions.
Core math problem & intuitions
- Many recall seeing similar “rolling circle/coin” problems in contests and school; lots admit they originally got it wrong.
- Multiple intuitions are discussed for why the small circle makes 4 revolutions when rolling outside a circle three times its radius:
- Think of distance traveled by the small circle’s center (circumference of a larger circle with radius R+r), divide by its own circumference.
- Visualize a polygon (e.g., triangle/square) and track how the disk “turns corners”; the sum of exterior angles gives the “extra” rotation, which persists in the circle limit.
- Picture the small disc as a unicycle wheel rolling on a curved track: one set of rotations for forward distance, plus one full “turn” to follow the loop.
- Shrink the inner circle toward a point: even around a point of radius ~0, the rolling coin still makes one full turn, giving the “+1” term.
- Inside-rolling version: commenters explain the “−1” case via direction of rotation, shorter radial path, or distance traveled by the center (R−r).
Ambiguity of the SAT question
- Debate centers on what “revolutions” means:
- External observer counting full 360° spins → answer 4.
- Comparing arc lengths along the tangential contact → answer 3.
- Astronomical-style “revolution around another body” → answer 1.
- Many argue the wording is too vague for a high-stakes test; multiple internally consistent interpretations exist, so “everyone got it wrong” is seen as misleading.
Scoring and fairness
- The flawed question was reportedly thrown out and all affected tests rescored.
- Some wanted “max(old, new)” scores; others argue that keeping any points from an invalid question is unfair.
- Several note how even small score shifts can matter near admissions cutoffs, and criticize releasing scores before a formal review period.
Education, testing, and vagueness
- Some see vagueness in math problems as a feature: it tests reading, background knowledge, and “common sense.”
- Others see it as cultural bias and training students to match test-writer assumptions rather than think independently.
- Broader debate touches on Common Core, decentralized curricula, inequality, magnet schools, and whether mass education can realistically approximate personalized tutoring.
Video format and sidereal connection
- Many liked that the video goes beyond the SAT story into sidereal vs solar time and planetary motion, viewing the toy problem as a gateway to astronomy.
- Others find the 18-minute, suspense-driven format padded or clickbaity and prefer concise written explanations (NYT/Scientific American).
- Some express mixed feelings about the channel more broadly: strong production and engaging topics, but occasional lack of nuance or overly dramatic framing.