1. The numbers $12, 14, 37$ and $65$ represent one of the solutions to the equation $x y - x z + y t = 182$. Determine which value each of these numbers represents for the variables.
1. Let's represent the given equation in the form $x(y-z)+y t=2 \cdot 7 \cdot 13$.

If $x=14$, then the product $y t$, formed in any way from the numbers 12, 37, and 65, does not divide by 7, and therefore equation (1) will not be valid. Similarly, we can verify that $x \neq 65$. If we rewrite the given equation as $y(x+t)-x z=2 \cdot 7 \cdot 13$, we similarly verify that $y \neq 14$ and $y \neq 65$. Therefore, the combinations of values for $x$ and $y$ to be tested are: $x=12, y=37$ or $x=37, y=12$. By substitution, we find that the equation is satisfied only when $x=12, y=37, z=65, t=14$.