Question:medium
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).
The last letter of the English alphabet that the first word of a sentence in the word game can begin with is
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).
The last letter of the English alphabet that the first word of a sentence in the word game can begin with is
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).
The last letter of the English alphabet that the first word of a sentence in the word game can begin with is
Show Hint
Work backward from "z": a sentence needs enough letters left in the alphabet after the starting letter to place all six words, three per letter at most.
Updated On: Jul 10, 2026
- t
- w
- x
- y
Show Solution
The Correct Option is C
Solution and Explanation
Instead of testing letters one by one from "z" downward, treat it as a room-counting problem: six words need to be placed, at most three per starting letter, moving strictly forward through the alphabet from wherever the first word starts. So the real question is: what is the latest starting letter that still leaves enough letters ahead of it to "hold" the remaining words?
- t: starting at "t" leaves "u, v, w, x, y, z" still ahead, far more room than six words need. This works, but it is not the LATEST such letter.
- w: starting at "w" leaves "x, y, z" ahead, again more than enough room for six words split three-and-three. This also works, but it may still not be the latest.
- x: starting at "x" leaves exactly "y" and "z" ahead of it, two letters. Three words can begin with "x" itself, and the remaining three words can be spread across "y" and "z" within the three-per-letter cap. Six words fit exactly.
- y: starting at "y" leaves only "z" ahead of it, a single letter. Three words can begin with "y", but the last three words then have to be squeezed into "z" while the sentence still needs room to keep climbing, and no letter is left after "z". The six-word requirement cannot be met cleanly, so "y" is one letter too far.
The room available after "x" (two full letters, "y" and "z") is exactly enough to complete the sentence, while starting one letter later, at "y", leaves too little room. That makes "x" the latest possible starting letter.
Let's summarize:
- A sentence needs enough "letter room" after the starting letter to safely fit six words under the three-per-letter cap.
- "x" is the last letter with two full letters ("y" and "z") still ahead of it.
- "y" and "z" each leave too little alphabet ahead to complete all six words.
Thus, the last letter of the alphabet that the first word of a valid sentence can begin with is "x".
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