Subcontests
(7)A rhombus' vertices on another rhombus' boundary
Let ABCD be a rhombus where ∠DAB=60∘, and P be the intersection between AC and BD. Let Q,R,S be three points on the boundary of ABCD such that PQRS is a rhombus. Prove that exactly one of Q,R,S lies on one of A,B,C,D. Solving a puzzle-like problem
Nine of the numbers 4,5,6,7,8,12,13,16,18,19 are going to be inputted to the empty cells in the following table:
\begin{array} {|c|c|c|} \cline{1-3}
10 & & \\ \cline{1-3}
& & 9 \\ \cline{1-3}
& 3 & \\ \cline{1-3}
11 & & 17 \\ \cline{1-3}
& 20 & \\ \cline{1-3}
\end{array}
such that each row sums to the same number, and each column sums to the same number. Determine all possible arrangements.