To solve this problem, we need to determine the minimum number of sock pieces that must be drawn to guarantee obtaining at least five pairs of non-white socks and four pairs of non-blue socks.

1. Define the Requirements:

   • We need 5 pairs of non-white socks. This means we need 5 pairs of red socks since white socks are excluded.
   • We also need 4 pairs of non-blue socks. This translates to needing 4 pairs of red or white socks (since blue socks are excluded).

2. Step-by-Step Solution:

   • Since each pair consists of 2 socks, getting 5 pairs of red socks requires at least $5 \times 2 = 10$ red socks.
   • To get 4 pairs of non-blue socks, we could get either red or white socks. However, to ensure 4 pairs (8 socks), we need to consider the worst case of drawing extra blue socks.

3. Worst-Case Scenario:

   • The worst case involves drawing as many unwanted colors as possible.
   • To satisfy the requirement of non-blue and non-white socks, we would encounter scenarios where we may draw extra white or blue socks.

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