Problem Statement:
There are boxes containing 5, 7, 14, 16, 18, and 29 balls of either red or blue color. Some boxes contain only red balls, and others contain only blue balls. A salesman sold one box and then claimed that he has the same number of red balls left as that of blue balls. Which box did he sell?

Explanation:

To solve this problem, we need to analyze the number of red and blue balls in each box and determine which box satisfies the salesman's claim.

Let's consider each box one by one and analyze the possible scenarios:

1. Box with 5 balls:
- If this box contains only red balls, the salesman cannot have an equal number of red and blue balls left.
- If this box contains only blue balls, the salesman cannot have an equal number of red and blue balls left.
- Hence, the box with 5 balls does not satisfy the salesman's claim.

2. Box with 7 balls:
- If this box contains only red balls, the salesman cannot have an equal number of red and blue balls left.
- If this box contains only blue balls, the salesman cannot have an equal number of red and blue balls left.
- Hence, the box with 7 balls does not satisfy the salesman's claim.

3. Box with 14 balls:
- If this box contains only red balls, the salesman cannot have an equal number of red and blue balls left.
- If this box contains only blue balls, the salesman cannot have an equal number of red and blue balls left.
- Hence, the box with 14 balls does not satisfy the salesman's claim.

4. Box with 16 balls:
- If this box contains only red balls, the salesman cannot have an equal number of red and blue balls left.
- If this box contains only blue balls, the salesman cannot have an equal number of red and blue balls left.
- Hence, the box with 16 balls does not satisfy the salesman's claim.

5. Box with 18 balls:
- If this box contains only red balls, the salesman cannot have an equal number of red and blue balls left.
- If this box contains only blue balls, the salesman cannot have an equal number of red and blue balls left.
- Hence, the box with 18 balls does not satisfy the salesman's claim.

6. Box with 29 balls:
- If this box contains only red balls, the salesman cannot have an equal number of red and blue balls left.
- If this box contains only blue balls, the salesman cannot have an equal number of red and blue balls left.
- Hence, the box with 29 balls does not satisfy the salesman's claim.

Based on the analysis above, none of the boxes satisfy the salesman's claim. Therefore, it is not possible to determine which box the salesman sold based on the given information.

Conclusion:
The salesman's claim cannot be true as none of the boxes fulfill the condition of having an equal number of red and blue balls left. Hence, the answer is inconclusive.