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MathNet 2000 — Math Olympiad Vault Question 153

Math Olympiad Vault · MathNet 2000 — Math Olympiad Vault

Question 153

We want to measure the length of a motor-racing circuit using a car whose odometer starts at zero and records kilometres but not hundreds of metres. What is the smallest $n$ such that, by looking only at the odometer after lap $n$, the driver can know the circuit length with an error below 30 metres?

(A) $0\lt n\le10$
(B) $10\lt n\le20$
(C) $20\lt n\le30$
(D) $30\lt n\le40$
(E) $40\lt n\le50$.