I developed a puzzle for which I am seeking an EFFICIENT algorithm (I searched Google but did not find this puzzle in the literature, ):
You have $k$ rationals, $n_1/d_1, n_2/d_2, ..., n_k/d_k$.
Query: Is there a way to flip some fractions and get 1 when multiplying all $k$ rationals $\prod_{i=1}^{k} n_i/d_i$$\prod_{i=1}^{k} n_i/d_i=1$ (flip turns a rational upside down).
Here is a solvable instance: 243/16, 81/32, 27/162, 8/54, 432/128, 648/36
Is there an efficient algorithm? or Is it NP-complete?