In the English alphabet written from A to Z, which letter lies exactly in the middle between the 13th letter from the left and the 4th letter from the right?

Introduction / Context:
This question asks you to locate two reference letters in the alphabet based on positional descriptions and then determine which letter lies exactly midway between them. It tests comfort with ordinal positions in the alphabet and simple averaging to find a central position.

Given Data / Assumptions:
• The alphabet is A, B, C, ..., Y, Z (26 letters).
• We need the 13th letter from the left and the 4th letter from the right.
• After finding these two letters, we must find the letter that lies in the middle of them in terms of alphabet position.

Concept / Approach:
The main concepts are position counting and finding a midpoint. The 13th from the left is straightforward. For the 4th from the right, we convert it to a position from the left by using the fact that right position r corresponds to left position 27 - r in a 26 letter alphabet. Once we have the two positions as numbers, their midpoint is simply the average of the two indices. The letter at this average index is the required middle letter.

Step-by-Step Solution:
Step 1: List positions from left: A (1), B (2), ..., M (13), ..., W (23), X (24), Y (25), Z (26).Step 2: Find the 13th letter from the left. This letter is M.Step 3: Find the 4th letter from the right. The rightmost letter is Z, so 1st from right is Z (26), 2nd from right is Y (25), 3rd from right is X (24) and 4th from right is W (23).Step 4: We now have positions 13 (M) and 23 (W). To find the middle position, compute the average: (13 + 23) / 2 = 36 / 2 = 18.Step 5: The 18th letter from the left in the alphabet is R (A is 1, so R is 18).Step 6: Therefore, R is exactly in the middle between M and W.

Verification / Alternative check:
You can verify by counting letters between M and W. From M to W, inclusive, the sequence is M (13), N (14), O (15), P (16), Q (17), R (18), S (19), T (20), U (21), V (22), W (23). There are 11 letters in this inclusive range, and the 6th letter in that mini sequence is R. Since it is equidistant from both ends of that sub sequence, it is indeed the middle letter.

Why Other Options Are Wrong:
• I: I is at position 9 and lies closer to the beginning of the alphabet, far from the midpoint between positions 13 and 23.
• J: J is at position 10 and again does not sit halfway between 13 and 23.
• S: S is at position 19, one step to the right of R, and would correspond to having unequal distances from M and W.
• T: T is at position 20 and lies even further to the right, increasing the imbalance, so it cannot be the exact middle.

Common Pitfalls:
Students sometimes miscalculate the 4th from the right or forget to convert it to a left position, leading to wrong endpoints. Others take the letter halfway in terms of literal count rather than position, which can create off by one errors. Using numeric positions and averages helps eliminate such confusion.

Final Answer:
The letter that lies exactly in the middle between the 13th letter from the left and the 4th letter from the right is R.