6.1: Finding the Complementary Letter for a Single Letter

 6.1: Finding the Complementary Letter for a Single Letter

This type involves finding the mirror or complementary letter for a given letter or vice versa.

Problem 1

Question: What is the complementary letter of G?

Solution Process:

• G is the 7th letter in the alphabet (A=1, ..., G=7).
• Complementary position:

  $27 - 7 = 20$27 - 7 = 20

  .
• 20th letter: A=1, B=2, ..., T=20.

Solution: T

Detailed Explanation:

• The mirror rule pairs the nth letter with the (27-n)th letter.
• For G (7th), compute 27-7=20, which is T.
• Alternatively, use the mirror pairs: AZ, BY, ..., GT (7th from start 7th from end).
• This tests basic application of the mirror formula.

Problem 2

Question: What is the complementary letter of M?

Solution Process:

• M = 13th letter.
• Complementary position:

  $27 - 13 = 14$27 - 13 = 14

  .
• 14th letter: A=1, ..., N=14.

Solution: N

Detailed Explanation:

• M (13th) mirrors to 27-13=14, which is N.
• Mirror pairs confirm: AZ, BY, ..., MN (13th 14th).
• This tests the symmetry around the alphabet’s midpoint (M and N are central).

Problem 3

Question: If the complementary letter of a letter is Q, what is the original letter?

Solution Process:

• Q = 17th letter.
• Complementary position:

  $27 - n = 17$27 - n = 17

  . Solve:

  $n = 27 - 17 = 10$n = 27 - 17 = 10

  .
• 10th letter: A=1, ..., J=10.

Solution: J

Detailed Explanation:

• Q is the 17th letter, so the original letter’s position ( n ) satisfies 27-n=17, giving n=10 (J).
• Mirror pairs: AZ, ..., JQ (10th 17th).
• This tests reversing the mirror transformation.

Problem 4

Question: What is the complementary letter of Z?

Solution Process:

• Z = 26th letter.
• Complementary position:

  $27 - 26 = 1$27 - 26 = 1

  .
• 1st letter: A.

Solution: A

Detailed Explanation:

• Z (26th) mirrors to 27-26=1, which is A.
• The pair AZ is the first mirror pair, confirming the solution.
• This tests the edge case of the alphabet’s last letter.

Problem 5

Question: What is the complementary letter of A?

Solution Process:

• A = 1st letter.
• Complementary position:

  $27 - 1 = 26$27 - 1 = 26

  .
• 26th letter: Z.

Solution: Z

Detailed Explanation:

• A (1st) mirrors to 27-1=26, which is Z.
• The pair AZ is fundamental to the mirror rule.
• This tests the other edge case (first letter).

Problem 6

Question: If the complementary letter of a letter is I, what is the original letter?

Solution Process:

• I = 9th letter.
• Complementary position:

  $27 - n = 9$27 - n = 9

  . Solve:

  $n = 27 - 9 = 18$n = 27 - 9 = 18

  .
• 18th letter: A=1, ..., R=18.

Solution: R

Detailed Explanation:

• I (9th) implies the original letter’s position is 27-9=18, which is R.
• Mirror pairs: AZ, ..., IR (9th 18th).
• This tests the reverse mapping for a mid-alphabet letter.

Problem 7

Question: What is the complementary letter of P?

Solution Process:

• P = 16th letter.
• Complementary position:

  $27 - 16 = 11$27 - 16 = 11

  .
• 11th letter: A=1, ..., K=11.

Solution: K

Detailed Explanation:

• P (16th) mirrors to 27-16=11, which is K.
• Mirror pairs: AZ, ..., KP.
• This tests a letter in the second half of the alphabet.

Problem 8

Question: Are B and Y complementary letters?

Solution Process:

• B = 2nd letter. Complementary position:

  $27 - 2 = 25$27 - 2 = 25

  . 25th letter = Y.
• Y = 25th letter. Complementary position:

  $27 - 25 = 2$27 - 25 = 2

  . 2nd letter = B.
• Since BY, they are complementary.

Solution: Yes

Detailed Explanation:

• B (2nd) mirrors to 27-2=25 (Y), and Y (25th) mirrors to 27-25=2 (B).
• The pair BY confirms they are complementary.
• This tests verifying a mirror pair.

Problem 9

Question: What is the complementary letter of X?

Solution Process:

• X = 24th letter.
• Complementary position:

  $27 - 24 = 3$27 - 24 = 3

  .
• 3rd letter: C.

Solution: C

Detailed Explanation:

• X (24th) mirrors to 27-24=3, which is C.
• Mirror pairs: AZ, BY, CX.
• This tests a letter near the end of the alphabet.

Problem 10

Question: If the complementary letter is E, what is the original letter?

Solution Process:

• E = 5th letter.
• Complementary position:

  $27 - n = 5$27 - n = 5

  . Solve:

  $n = 27 - 5 = 22$n = 27 - 5 = 22

  .
• 22nd letter: A=1, ..., V=22.

Solution: V

Detailed Explanation:

• E (5th) implies the original letter’s position is 27-5=22, which is V.
• Mirror pairs: AZ, ..., EV.
• This tests reverse mapping for an early letter