MathDB

Problem 5

Part of 2019 LIMIT Category A

Problems(2)

arccos sum

Source: LIMIT 2019 CAS1 P5

4/28/2021
If ∑i=1ncos⁡−1(αi)=0\sum_{i=1}^n\cos^{-1}(\alpha_i)=0, then find ∑i=1nαi\sum_{i=1}^n\alpha_i. <spanclass=′latex−bold′>(A)</span> n2<span class='latex-bold'>(A)</span>~\frac n2 <spanclass=′latex−bold′>(B)</span> n<span class='latex-bold'>(B)</span>~n <spanclass=′latex−bold′>(C)</span> nπ<span class='latex-bold'>(C)</span>~n\pi <spanclass=′latex−bold′>(D)</span> nπ2<span class='latex-bold'>(D)</span>~\frac{n\pi}2
trigonometryalgebraSummation
placing numbers in chessboard

Source: LIMIT 2019 CAS2 P5

4/28/2021
6464 numbers (not necessarily distinct) are placed on the squares of a chessboard such that the sum of the numbers in every 2×22\times2 square is 77. What is the sum of the four numbers in the corners of the board?
combinatorics