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Nov 23, 2023 at 19:23 comment added mathematrucker When our Putnam prof was prepping us for the 1981 exam (he wasn't involved with its creation), he said "it always has a Lagrange multiplier problem." Luckily for me, his prediction came true:$$$$$\textbf{B-2.}$ Determine the minimum value of $$(r-1)^2 + \left(\frac{s}{r} - 1\right)^2 + \left(\frac{t}{s} - 1\right)^2 + \left(\frac{4}{t} - 1\right)^2$$ for all real numbers $r,s,t$ with $1\leq r\leq s\leq t\leq4.$$$$$ Fewer than 2% of contestants got a perfect $10$ on the problem. Thanks to my professor's prescience, I was one of them.
Jan 27, 2017 at 8:16 history edited Aryeh Kontorovich CC BY-SA 3.0
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S Jan 27, 2017 at 8:10 history answered Aryeh Kontorovich CC BY-SA 3.0
S Jan 27, 2017 at 8:10 history made wiki Post Made Community Wiki by Aryeh Kontorovich