If each letter of the English alphabet is interchanged with the letter fourteen positions away from it (so that A and N swap, B and O swap, and so on until M and Z swap), then in this new alphabet which letter is seventh to the right of the thirteenth letter from the right?

Introduction / Context:
This problem modifies the usual alphabet using a fixed swapping rule and then asks for relative positions in the new order. The swaps are between letters fourteen positions apart, which effectively rearranges the alphabet into a new sequence. Once this sequence is known, the task is to locate a letter based on counting from the right and then moving some steps to the right. Such questions test your ability to follow transformations carefully and then perform positional reasoning.

Given Data / Assumptions:
We start with the normal alphabet A to Z. The rule is that the first letter A swaps with the fourteenth letter N, the second letter B swaps with the fifteenth letter O, and this continues until the thirteenth letter M swaps with the twenty sixth letter Z. After this swapping, a new alphabetic sequence is formed. In this new sequence, we must find the thirteenth letter from the right. Then we must identify the letter that is seventh to the right of that letter. We assume a single fixed new order arises from these swaps.

Concept / Approach:
The easiest way is to write the new sequence directly. Positions 1 to 13 (A to M) swap with positions 14 to 26 (N to Z). This means the new first letter becomes N, the new second letter becomes O, and so on. After constructing the full new sequence, we can find the thirteenth letter from the right by calculating its index from the left. Since there are 26 letters, the thirteenth from the right is at position 26 minus 13 plus 1 from the left. Finally, moving seven steps to the right means adding seven to this index and reading off the resulting letter.

Step-by-Step Solution:
Write the original alphabet positions: 1 A, 2 B, 3 C, 4 D, 5 E, 6 F, 7 G, 8 H, 9 I, 10 J, 11 K, 12 L, 13 M, 14 N, 15 O, 16 P, 17 Q, 18 R, 19 S, 20 T, 21 U, 22 V, 23 W, 24 X, 25 Y, 26 Z. Apply the swapping rule: positions 1 and 14 swap, 2 and 15 swap, and so on up to positions 13 and 26. After swapping, the new sequence from position 1 to 26 is: N O P Q R S T U V W X Y Z A B C D E F G H I J K L M. To find the thirteenth letter from the right, calculate its left index as 26 - 13 + 1 = 14. Looking at the new sequence, position 14 is occupied by A. Now we must find the letter seventh to the right of this A, which is at position 14. So we compute 14 + 7 = 21. The 21st letter in the new sequence is H, since the letters at positions 14 to 21 are A, B, C, D, E, F, G, H.

Verification / Alternative check:
For verification, you can count directly from the right end of the new sequence. The new sequence is N O P Q R S T U V W X Y Z A B C D E F G H I J K L M. Counting from the right, M is 1st, L is 2nd, K is 3rd, J is 4th, I is 5th, H is 6th, G is 7th, F is 8th, E is 9th, D is 10th, C is 11th, B is 12th and A is 13th from the right. This matches our earlier conclusion that A is the thirteenth from the right. Moving seven positions to the right from A at position 14 still takes us to position 21, which is H. Both counting methods agree, confirming that H is correct.

Why Other Options Are Wrong:
U, G, I and K all occupy different positions in the new sequence. U appears earlier in the right half of the new alphabet and does not satisfy the positional calculation we performed. G and I are close to H but correspond to positions 20 and 22 respectively, not 21. K is further to the right and also does not line up with the seventh to the right of the thirteenth from the right. Therefore, none of these letters matches the required position, and only H fits the computed index exactly.

Common Pitfalls:
A common mistake is to misunderstand the swapping rule and think that A swaps with Z, B with Y and so on, which is a different transformation. Another pitfall is to miscalculate the index of the thirteenth from the right, sometimes forgetting to add 1 after subtracting from 26. Some candidates also try to track everything mentally without writing the new sequence, which increases the chance of mixing up letter positions. To avoid such errors, clearly write the transformed alphabet, use the 26 - k + 1 formula for converting right positions to left positions and count carefully. Double checking the count from the opposite end helps catch missteps.

Final Answer:
In the transformed alphabet, the letter that is seventh to the right of the thirteenth letter from the right is H.