Let \( f(n) \) denote the number of possible sequences of length \( n \), where each term is either \(0, 1,\) or \(-1\), such that the product of every three consecutive numbers is nonnegative. Compute \( f(33)\).
Let \(A= [a_{ij}]_{1\leq i,j\leq 5}\) be a \(5\times 5\) positive definite (real) matrix. Show that the matrix \([a_{ij}/(i+j)]\) is also positive definite.
The best solution was submitted by 김찬우 (연세대학교 수학과 22학번, +4). Congratulations!
Here is the best solution of problem 2024-16.
Other solutions were submitted by 김준홍 (KAIST 수리과학과 석박통합과정, +3), 노희윤 (KAIST 수리과학과 석박통합과정, +3), 서성욱 (대전 동산고 3학년, +3), 신민규 (KAIST 새내기과정학부 24학번, +3), 양준혁 (KAIST 수리과학과 20학번, +3), 이명규 (KAIST 전산학부 20학번, +3), 최정담 (KAIST 디지털인문사회과학부 석사과정, +3).