# Unnamed Problem – 1 (Number theory)

Let $X = \{x_1, x_2,\ldots,x_n | x_i \in Z \;\forall i = 1,\ldots,n \}$ and associated with each set X is another set $Y_x = \{y_1, y_2,\ldots,y_m\; |\; y_l = \sum_{i = 1,\ldots,n}x_if_i,\; f_i \in \{0,1\},\; \sum_{i} f_i > 0 \}$.

Let $Y'_x$ be a subset of $Y_x$ and is defined as, $Y'_x = \{y_f | y_f = \sum_{i = 1,\ldots,n}x_if_i,\;f_g = 1,\; 1 \leq g \leq n\}$

The question is to write an algorithm that says for any given $y_d \in Y_x$ whether $y_d \in Y'_x$