MathDB

25

Part of 2016 ASDAN Math Tournament

Problems(1)

2016 Guts #25

Source:

8/14/2022
Find the best rational approximation xx to 20163\sqrt[3]{2016} such that ∣x−20163∣|x-\sqrt[3]{2016}| is as small as possible. You may either find an x=abx=\tfrac{a}{b} where a,ba,b are coprime integers or find a decimal approximation. Let CC be the actual answer and AA be the answer you submit. Your score will be given by ⌈10+16.50.1+e30∣A−C∣⌉\lceil10+\tfrac{16.5}{0.1+e^{30|A-C|}}\rceil, where ⌈x⌉\lceil x\rceil denote the smallest integer which is ≥x\geq x.
2016Guts Round