Thirty-two players ranked 1 to 32 are playing in a knockout tournament. Assume that in every match between any two players the better ranked player wins, the probability that ranked 1 and ranked 2 players are winner and runner up respectively is p, then the value of `[2//p]` is, where [.] represents the greatest integer function,_____.

Explanation

To solve the problem, we need to find the probability \( p \) that the player ranked 1 wins the tournament and player ranked 2 is the runner-up.

### Step-by-Step Solution:

1. **Understanding the Tournament Structure**:
In a knockout tournament with 32 players, each match eliminates one player. The tournament proceeds in rounds until one player remains as the winner.

2. **Condition for Ranked 1 and Ranked 2**:
For player ranked 1 to be the winner and player ranked 2 to be the runner-up, they must not face each other in any round. If they are paired against each other, one will eliminate the other.

3. **Calculating the Probability**:
- In the first round, player ranked 1 can face any of the 31 other players. For player ranked 2 to avoid facing player ranked 1, they must be paired with one of the other 30 players. Thus, the probability that player ranked 1 and player ranked 2 do not face each other in the first round is:
\[ \frac{30}{31} \]
- In the subsequent rounds, the same logic applies. After the first round, there will be 16 players left (including players ranked 1 and 2). For player ranked 2 to avoid facing player ranked 1 in the second round, they must be paired with one of the other 14 players. Thus, the probability for the second round is:
\[ \frac{14}{15} \]
- Continuing this reasoning, we find the probabilities for the next rounds:
- Third round:
\[ \frac{6}{7} \]
- Fourth round:
\[ \frac{2}{3} \]

4. **Combining the Probabilities**:
The total probability \( p \) that player ranked 1 wins and player ranked 2 is the runner-up is the product of the probabilities from each round:
\[ p = \frac{30}{31} \times \frac{14}{15} \times \frac{6}{7} \times \frac{2}{3} \]

5. **Calculating \( p \)**:
- Calculate the product step by step:
\[ p = \frac{30 \times 14 \times 6 \times 2}{31 \times 15 \times 7 \times 3} \]
- First, calculate the numerator:
\[ 30 \times 14 = 420 \]
\[ 420 \times 6 = 2520 \]
\[ 2520 \times 2 = 5040 \]
- Now, calculate the denominator:
\[ 31 \times 15 = 465 \]
\[ 465 \times 7 = 3255 \]
\[ 3255 \times 3 = 9765 \]
- Thus, we have:
\[ p = \frac{5040}{9765} \]

6. **Simplifying \( p \)**:
We can simplify \( \frac{5040}{9765} \) by finding the greatest common divisor (GCD) if necessary, but for this problem, we can directly use the fraction.

7. **Finding \( \frac{2}{p} \)**:
\[ \frac{2}{p} = \frac{2 \times 9765}{5040} = \frac{19530}{5040} \]
- Now simplify \( \frac{19530}{5040} \):
\[ \frac{19530 \div 630}{5040 \div 630} = \frac{31}{8} \]

8. **Finding the Greatest Integer Function**:
The greatest integer function \( \left\lfloor \frac{31}{8} \right\rfloor = 3 \).

### Final Answer:
The value of \( \left\lfloor \frac{2}{p} \right\rfloor \) is \( 3 \).