Daniel, Clarence, and Matthew split a \$20.20 dinner bill so that Daniel pays half of what Clarence pays. If Daniel pays \$6.06, what is the ratio of Clarence's pay to Matthew's pay?

[i]Proposed by Henry Ren[/i]
1. **Determine Clarence's payment:**
   Since Daniel pays half of what Clarence pays, we can set up the equation:
   \[
   D = \frac{1}{2}C
   \]
   Given that Daniel pays \$6.06, we substitute \(D = 6.06\) into the equation:
   \[
   6.06 = \frac{1}{2}C
   \]
   Solving for \(C\):
   \[
   C = 6.06 \times 2 = 12.12
   \]
   Therefore, Clarence pays \$12.12.

2. **Determine Matthew's payment:**
   The total bill is \$20.20. We know the payments of Daniel and Clarence, so we can find Matthew's payment by subtracting their payments from the total:
   \[
   M = 20.20 - D - C
   \]
   Substituting the known values:
   \[
   M = 20.20 - 6.06 - 12.12 = 2.02
   \]
   Therefore, Matthew pays \$2.02.

3. **Calculate the ratio of Clarence's payment to Matthew's payment:**
   The ratio of Clarence's payment to Matthew's payment is:
   \[
   \frac{C}{M} = \frac{12.12}{2.02}
   \]
   Simplifying the ratio:
   \[
   \frac{12.12}{2.02} = \frac{1212}{202} = \frac{6}{1}
   \]
   Therefore, the ratio of Clarence's payment to Matthew's payment is 6:1.

The final answer is \(\boxed{6:1}\)