Letter and alphabet analogies

Learning outcome

Track each letter by its alphabet position, then repeat the same shift or the same opposite-letter rule.

Concepts and reasons

Give the letters positions A = 1 through Z = 26. A letter analogy usually moves every letter by the same number of steps, or pairs each letter with the letter whose position adds up to 27.

A forward shift of 1 sends A to B, B to C, and Z would send past the alphabet, which this module does not use. The word CAT shifted forward by 1 becomes DBU, because C, A and T each move one place.

Opposite letters add to 27: A and Z, B and Y, C and X, D and W. The opposite of a letter in position n is the letter in position 27 − n. The opposite of D, position 4, is W, position 23. It is not the letter 26 − n, which would incorrectly give V.

When the first pair is two letters, such as AZ, check whether they are opposites before treating them as a two-step jump. AZ is an opposite pair. The next opposite pairs in order are BY, CX and DW.

Worked examples

Example 1. CAT : DBU :: PEN : ? Each letter of CAT moves forward by 1. P, E and N move forward by 1 to Q, F and O. The answer is QFO. Moving backward gives ODM, which copies the size of the step but not the direction.

Example 2. A : Z :: D : ? A and Z are opposites, since 1 + 26 = 27. D is position 4, and 27 − 4 = 23, which is W.

Example 3. AZ : BY :: CX : ? Each pair is a letter followed by its opposite, and the first letters run A, B, C. The next first letter is D, and its opposite is W. The answer is DW.

Common traps

A backward shift is not the same rule as a forward shift. The opposite of a letter uses 27 minus its position, not 26 minus its position. In a three-letter word, every letter must move. Changing only the first letter fails the rule.

Practice questions

1. DOG : EPH :: BAT : ?
2. What is the opposite letter of G?
3. ACE : BDF :: GIK : ? Name the shift.

Answers and explanations

1. Each letter moves forward by 1. B, A and T become C, B and U, so the answer is CBU.
2. G is position 7. Then 27 − 7 = 20, which is T.
3. Each letter of ACE moves forward by 1 to make BDF. G, I and K move forward by 1 to H, J and L, so the answer is HJL.

Analogy

A : Z :: D : W.

Positions 1 and 26 add to 27, so they are opposites. D is position 4, and 27 minus 4 is 23, which is W.

Quick reference

• A = 1 and Z = 26.
• A forward shift of 1 moves every letter one place, as CAT to DBU.
• Opposite position = 27 minus the letter position.
• 26 minus the position is one letter short of the opposite.