MathDB
2016 Algebra Tiebreaker #3

Source:

August 8, 2022
2016Algebra Tiebreaker

Problem Statement

Denote the dot product of two sequences ⟨x1,…,xn⟩\langle x_1,\dots,x_n\rangle and ⟨y1,…,yn⟩\langle y_1,\dots,y_n\rangle to be x1y1+x2y2+⋯+xnyn.x_1y_1+x_2y_2+\dots+x_ny_n. Let ⟨a1,…,an⟩\langle a_1,\dots,a_n\rangle and ⟨b1,…,bn⟩\langle b_1,\dots,b_n\rangle be two sequences of consecutive integers (i.e. for 1≤i,i+1≤n1\leq i,i+1\leq n, ai+1=ai+1a_i+1=a_{i+1} and similarly for bib_i). Minnie permutes the two sequences so that their dot product, mm, is minimized. Maximilian permutes the two sequences so that their dot product, MM, is maximized. Given that m=4410m=4410 and M=4865M=4865, compute nn, the number of terms in each sequence.
Back to ProblemsView on AoPS