Question

In a game, a "word" is any combination of at least five letters of the English alphabet (the word does not have to have a meaning). A "sentence" in this game consists of exactly six such words, and it must satisfy all of the following rules:
1. The six words are written from left to right on a single line, in strictly increasing alphabetical order.
2. The sentence may start with any word. Each successive word is obtained from the word right before it by applying exactly ONE of three operations: deleting one letter, adding one letter, or replacing one letter with another letter.
3. At most three of the six words can begin with the same letter.
4. Apart from the first word, every word must be formed using an operation different from the one used to form the word immediately before it (so the same operation can never be used twice in a row).

Which one of the following could be a sentence in the word game?

• A. Bzaeak, blaeak, laeak, paeak, paea, paean
• B. Crobek, croeek, roeek, soeek, sxoeek, xoeek
• C. Doteam, goleam, golean, olean, omean, omman
• D. Feted, freted, reted, seted, seteg, aseteg

Hint:

Check each option against all four rules together (alphabetical order, one edit per step, no repeated edit type, and a cap of three same-starting-letter words) - most options fall on just one of these checks.

Answer 1

The Correct Option is B

Step 1: Restate the rules.
Every option lists six words that are meant to form one "sentence" in the game. To find the valid one, check each option against all four rules: the words must climb in strict alphabetical order, each word must come from the one before it by exactly one add, delete, or replace move, no more than three words can share a starting letter, and no operation can repeat back to back.

Step 2: Rule out option (AA).
The first word is "Bzaeak" and the second is "blaeak". Comparing the two words, "Bz..." and "bl..." do not climb in alphabetical order, because "l" comes before "z". So the second word is actually earlier in the alphabet than the first word, which breaks the ordering rule straight away.

Step 3: Rule out option (CC).
The first word "Doteam" turns into "goleam". Comparing the two words, both the first letter ("D" to "g") and the third letter ("t" to "l") have changed. A single operation can only change, add, or remove one letter at a time, so getting from "Doteam" to "goleam" needs at least two separate replacements. That is not allowed in one step, so option (CC) fails the single-operation rule.

Step 4: Rule out option (DD).
Follow the chain: "reted" becomes "seted" by replacing "r" with "s", a replace move. Then "seted" becomes "seteg" by replacing "d" with "g", again a replace move. Two replace moves back to back break the rule that every word must use an operation different from the one just before it. Option (DD) is out.

Step 5: Rule out option (EE).
Look at the starting letters of the six words: "Forod", "forol", "forols", "forpls" all start with "f", which is already four words beginning with the same letter. The rule allows at most three words to share a starting letter, so option (EE) is eliminated too.

Step 6: Confirm option (BB).
Check "Crobek, croeek, roeek, soeek, sxoeek, xoeek" against every rule. The words climb steadily in alphabetical order: Crobek, then croeek (later because "b" comes before "e" at the fourth letter), then roeek, soeek, sxoeek, xoeek, each one alphabetically after the one before. The operations used are: replace "b" with "e" (Crobek to croeek), delete "c" (croeek to roeek), replace "r" with "s" (roeek to soeek), add "x" (soeek to sxoeek), and delete "s" (sxoeek to xoeek). These five operations are replace, delete, replace, add, delete, and no two neighbouring operations match. The starting letters are C, C, r, s, s, x, so "C" and "s" each appear only twice, well within the limit of three. Every rule is satisfied.

Final Answer:
Option (BB) is the only list of six words that obeys the alphabetical order rule, the single-operation rule, the operation-alternation rule, and the shared-starting-letter limit at the same time. \[ \boxed{\text{Option B}} \]