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Omni-MATH / While waiting for their food at a restaurant in Harvard Square, Ana and Banana…

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problem

While waiting for their food at a restaurant in Harvard Square, Ana and Banana draw 3 squares $\square_{1}, \square_{2}, \square_{3}$ on one of their napkins. Starting with Ana, they take turns filling in the squares with integers from the set {1,2,3,4,5}\{1,2,3,4,5\} such that no integer is used more than once. Ana's goal is to minimize the minimum value MM that the polynomial a1x2+a2x+a3a_{1} x^{2}+a_{2} x+a_{3} attains over all real xx, where a1,a2,a3a_{1}, a_{2}, a_{3} are the integers written in $\square_{1}, \square_{2}, \square_{3}$ respectively. Banana aims to maximize MM. Assuming both play optimally, compute the final value of 100a1+10a2+a3100 a_{1}+10 a_{2}+a_{3}.
Plain-text mathematical notation (without MathML)
While waiting for their food at a restaurant in Harvard Square, Ana and Banana draw 3 squares $\square_{1}, \square_{2}, \square_{3}$ on one of their napkins. Starting with Ana, they take turns filling in the squares with integers from the set {1,2,3,4,5} such that no integer is used more than once. Ana's goal is to minimize the minimum value M that the polynomial a₁x²+a₂x+a₃ attains over all real x, where a₁,a₂,a₃ are the integers written in $\square_{1}, \square_{2}, \square_{3}$ respectively. Banana aims to maximize M. Assuming both play optimally, compute the final value of 100a₁+10a₂+a₃.
Original LaTeX notation
While waiting for their food at a restaurant in Harvard Square, Ana and Banana draw 3 squares $\square_{1}, \square_{2}, \square_{3}$ on one of their napkins. Starting with Ana, they take turns filling in the squares with integers from the set $\{1,2,3,4,5\}$ such that no integer is used more than once. Ana's goal is to minimize the minimum value $M$ that the polynomial $a_{1} x^{2}+a_{2} x+a_{3}$ attains over all real $x$, where $a_{1}, a_{2}, a_{3}$ are the integers written in $\square_{1}, \square_{2}, \square_{3}$ respectively. Banana aims to maximize $M$. Assuming both play optimally, compute the final value of $100 a_{1}+10 a_{2}+a_{3}$.

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Source and history

task_id
92eb312b-23d2-5d7e-843b-2da94b9c72ea
task_key
test--92eb312b-23d2-5d7e-843b-2da94b9c72ea
task_revision_id
1
config / split
/ test

Official source

initial import