A [i]trio [/i] is a set of three distinct integers such that two of the numbers are divisors or multiples of the third. Which [i]trio [/i] contained in $\{1, 2, ... , 2002\}$ has the largest possible sum? Find all [i]trios [/i] with the maximum sum.
1. **Identify the conditions for a trio:**
   A *trio* is a set of three distinct integers \(a, b, c\) such that two of the numbers are divisors or multiples of the third. We need to find the trio with the largest possible sum within the set \(\{1, 2, \ldots, 2002\}\).

2. **Analyze the possible cases:**
   - Case 1: \(a\) and \(b\) are divisors/multiples of \(c\).
   - Case 2: \(a\) and \(c\) are divisors/multiples of \(b\).
   - Case 3: \(b\) and \(c\) are divisors/multiples of \(a\).

3. **Evaluate Case 1:**
   - If \(a\) and \(b\) are divisors of \(c\), then \(b \leq \frac{c}{2}\) and \(a \leq \frac{c}{3}\).
   - Therefore, \(a + b + c \leq \frac{c}{3} + \frac{c}{2} + c = \frac{11c}{6}\).
   - Since \(c \leq 2002\), \(\frac{11c}{6} < 4004\).

4. **Evaluate Case 2:**
   - If \(a\) and \(c\) are divisors/multiples of \(b\), then \(a\) must divide \(b\) and \(b\) must divide \(c\).
   - This is a special case of Case 1, so the same upper bound applies.

5. **Evaluate Case 3:**
   - If \(b\) and \(c\) are multiples of \(a\), then \(b \leq c - a\).
   - Therefore, \(a + b + c \leq 2c \leq 4004\).

6. **Find the maximum sum:**
   - We can achieve \(4004\) by choosing \(c = 2002\), \(a + b = 2002\), and ensuring \(a\) is a divisor of \(2002\).

7. **List the divisors of 2002:**
   - The divisors of 2002 are \(1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286, 1001, 2002\).

8. **Form the trios:**
   - Exclude \(2002\) and \(1001\) since \(a, b, c\) must be distinct.
   - The valid trios are \((1, 2001, 2002), (2, 2000, 2002), (7, 1995, 2002), (11, 1991, 2002), (13, 1989, 2002), (14, 1988, 2002), (22, 1980, 2002), (26, 1976, 2002), (77, 1925, 2002), (91, 1911, 2002), (143, 1859, 2002), (154, 1848, 2002), (182, 1820, 2002), (286, 1716, 2002)\).

The final answer is \( \boxed{ (a, 2002-a, 2002) } \) where \(a = 1, 2, 7, 11, 13, 14, 22, 26, 77, 91, 143, 154, 182, 286\).