Word-formation count: Using each letter only once, how many meaningful English words can be formed from the letters D, L, E, I?

Difficulty: Easy

Correct Answer: Three

Explanation:


Introduction / Context:
This is a classic letter-bag problem. You have exactly the letters D, L, E, I (one each) and must determine how many standard English words can be formed, using each letter at most once. Such items check vocabulary breadth and systematic enumeration.


Given Data / Assumptions:

  • Letter multiset: {D, L, E, I}.
  • Each letter used once per word.
  • Count common-dictionary words; exclude proper nouns and obscure terms.


Concept / Approach:
Try natural arrangements with common patterns: initial consonant + vowel + consonant + vowel, or check well-known words. Three everyday words are well-attested: IDLE (adjective/verb), LIED (past of “lie” meaning “to be untruthful”; also a musical term “Lied,” but lowercase “lied” is valid past tense), and DELI (a delicatessen; widely accepted as a standard English noun). All three use each of the four letters exactly once.


Step-by-Step Solution:
1) Consider “IDLE”: I D L E ✓2) Consider “LIED”: L I E D ✓3) Consider “DELI”: D E L I ✓4) Search for additional common words (e.g., “diel” is technical; typically excluded). None add beyond three.


Verification / Alternative check:
All three (IDLE, LIED, DELI) appear in mainstream dictionaries and in everyday usage. No further common words arise without repeating letters or introducing new ones.


Why Other Options Are Wrong:
“None/One/Two” under-count the set. There are exactly three standard words.


Common Pitfalls:
Discarding “DELI” as an abbreviation. It is not; it is standard English for a delicatessen.


Final Answer:
Three

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