A customer ordered thirteen zingers. Zingers are placed in packages of four, three, or one. In how many different ways can this order be filled? The number of possible different ways is (Type a whole number.)

Step 1 ：The problem is asking for the number of ways to partition the number 13 into sums of 4, 3, and 1. This is a classic problem of integer partitioning, which can be solved using dynamic programming.

Step 2 ：We can create a 2D array dp[i][j] where i is the number of zingers and j is the number of types of packages. dp[i][j] will store the number of ways to partition i using j types of packages.

Step 3 ：We will initialize dp[i][0] = 0 for all i > 0 and dp[0][j] = 1 for all j >= 0.

Step 4 ：Then, for each i and j, we will calculate dp[i][j] as the sum of dp[i][j-1] (not using the jth type of package) and dp[i - package[j]][j] (using the jth type of package).

Step 5 ：Finally, dp[13][3] will give us the number of ways to partition 13 using all types of packages.

Step 6 ：\(\boxed{14}\) different ways to fill the order.