The numbers $12,14,37,65$ are one of the solutions of the equation $xy-xz+yt=182$. What number corresponds to which letter?
To solve the equation \( xy - xz + yt = 182 \) with the given numbers \( 12, 14, 37, 65 \), we need to determine which number corresponds to each variable \( x, y, z, t \).

1. **Assigning values to \( x \)**:
   Let's start by assigning \( x = 12 \). Then the equation becomes:
   \[
   12y - 12z + yt = 182
   \]

2. **Simplifying the equation**:
   Rearrange the equation to isolate \( yt \):
   \[
   12(y - z) + yt = 182
   \]

3. **Modulo operation**:
   To find \( yt \) in terms of \( \mod 12 \), we take the equation modulo 12:
   \[
   12(y - z) + yt \equiv 182 \pmod{12}
   \]
   Since \( 12(y - z) \equiv 0 \pmod{12} \), we have:
   \[
   yt \equiv 182 \pmod{12}
   \]
   Simplifying \( 182 \mod 12 \):
   \[
   182 \div 12 = 15 \text{ remainder } 2 \implies 182 \equiv 2 \pmod{12}
   \]
   Therefore:
   \[
   yt \equiv 2 \pmod{12}
   \]

4. **Testing possible values for \( y \) and \( t \)**:
   The remaining values are \( 14, 37, 65 \). We need to find \( y \) and \( t \) such that \( yt \equiv 2 \pmod{12} \).

   - If \( y = 14 \):
     \[
     14t \equiv 2 \pmod{12}
     \]
     Simplifying \( 14 \mod 12 \):
     \[
     14 \equiv 2 \pmod{12} \implies 2t \equiv 2 \pmod{12}
     \]
     Dividing both sides by 2:
     \[
     t \equiv 1 \pmod{6}
     \]
     Possible values for \( t \) are \( 1, 7, 13, \ldots \). Since \( t \) must be one of the given numbers, \( t = 65 \) (as \( 65 \equiv 1 \pmod{6} \)).

   - If \( y = 37 \):
     \[
     37t \equiv 2 \pmod{12}
     \]
     Simplifying \( 37 \mod 12 \):
     \[
     37 \equiv 1 \pmod{12} \implies t \equiv 2 \pmod{12}
     \]
     Possible values for \( t \) are \( 2, 14, 26, \ldots \). Since \( t \) must be one of the given numbers, \( t = 14 \).

5. **Assigning remaining values**:
   - If \( y = 14 \) and \( t = 65 \), then \( z = 37 \).
   - If \( y = 37 \) and \( t = 14 \), then \( z = 65 \).

6. **Verifying the solution**:
   Let's verify the solution \( x = 12, y = 37, z = 65, t = 14 \):
   \[
   12 \cdot 37 - 12 \cdot 65 + 37 \cdot 14 = 444 - 780 + 518 = 182
   \]
   The equation holds true.

The final answer is \( \boxed{ x = 12, y = 37, z = 65, t = 14 } \).