In the string prp qrp prr pqr qrp rpr qqr rpr qpr qrr qpr qpr, every third character from the left is replaced by numbers starting from 1. After this replacement, which symbol (letter or number) is 16th from the right?

Introduction / Context:
This problem combines counting and positional reasoning in a long string of letters. After every third letter is replaced by a number, we must identify the symbol that appears at a specific position from the right. The key ideas are careful counting and understanding how the replacement rule affects positions.

Given Data / Assumptions:

• Original sequence of letters: prp qrp prr pqr qrp rpr qqr rpr qpr qrr qpr qpr (twelve groups of three letters each).
• Spaces are only for readability; the sequence effectively has 36 positions.
• Every third character from the left (positions 3, 6, 9 and so on) is replaced by numbers starting from 1 in order.

Concept / Approach:
Each original letter occupies a position in a linear sequence of 36 characters. Replacing the letter at each third position with a number does not change the total number of positions; it only changes what symbol occupies those positions. We can therefore reason entirely with position indices. Once we know which position from the left corresponds to the 16th from the right, we can see whether that position is one of the replaced ones.

Step-by-Step Solution:
Step 1: There are twelve groups of three letters each, so the total length of the sequence is 12 × 3 = 36 symbols.Step 2: The 16th symbol from the right is the same as the (36 - 16 + 1)th symbol from the left, which is the 21st symbol.Step 3: The replacement rule covers every third position from the left: positions 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33 and 36.Step 4: Position 21 is one of these replaced positions, so it contains a number rather than a letter.Step 5: The first replaced position (3rd) is numbered 1, the second (6th) is 2, and so on. Thus the number at the nth replaced position is n.Step 6: Position 21 is the 7th replaced position (since 21 = 3 × 7). Therefore the number written there is 7.

Verification / Alternative check:
We can list the replaced positions together with their numbers: position 3 = 1, 6 = 2, 9 = 3, 12 = 4, 15 = 5, 18 = 6, 21 = 7, 24 = 8, 27 = 9, 30 = 10, 33 = 11, 36 = 12. This clearly shows that the 21st position from the left has the number 7 and thus corresponds to the 16th position from the right.

Why Other Options Are Wrong:
Options q and r would only be correct if the 21st position was not one of the replaced positions, which it is. The number 6 belongs at position 18, and any other number or letter does not match the systematic numbering pattern of every third position.

Common Pitfalls:
A common mistake is to miscount positions from the left or to assume that double digit numbers such as 10 occupy two positions, which is not the case here. Each replacement position holds a single symbol, representing the number for that place. Another error is forgetting to convert 16th from the right into its equivalent from the left before applying the replacement rule.

Final Answer:
After the described replacement, the symbol that is 16th from the right is the number 7.