The odd letter group

Learning outcome

Compare the gaps between letters and mark the group whose gaps do not match the other three.

Concepts and reasons

Give letters positions A = 1 through Z = 26. In ACE, C is two after A and E is two after C. The gap pattern is +2, +2. Three groups with the same gaps form the class. The group with a different gap is the odd one.

Opposite pairs are a second class. AZ, BY and CX each add to 27. A consecutive pair such as DE does not.

Worked examples

Example 1. ACE, BDF, CEG, MOR. ACE, BDF and CEG are +2, +2. M to O is +2, but O to R is +3. MOR is the odd group.

Example 2. AZ, BY, CX, DE. The first three are opposite pairs. D and E are neighbours, positions 4 and 5. DE is the odd group.

Common traps

Do not compare only the first letters. ACE and BDF start on different letters and still share +2, +2. The gap is the class, not the starting letter.

Practice questions

1. Which group is outside ACE, GIK, BDF, PRT if one of them is not +2, +2? Check each gap.
2. What is the position sum of an opposite pair?

Answers and explanations

1. A to C to E, G to I to K, and B to D to F are all +2, +2. P to R is +2 and R to T is +2, so PRT is also +2, +2. None of these four is outside that class.
2. Opposite letters have positions that add to 27.

Analogy

ACE, BDF, CEG, MOR.

Three groups step forward by 2 and then by 2. MOR steps by 2 and then by 3, so MOR is the odd group.

Quick reference

• Write the two gaps, such as +2, +2.
• Opposite letters add to 27: AZ, BY, CX, DW.
• The starting letter can change while the gap stays the same.
• A neighbour pair such as DE is not an opposite pair.