Introduction
In "Common Code for Multiple Words" problems, you are given codes for several short phrases or sentences and must deduce how individual words or tokens map to parts of those codes. These questions test your ability to compare multiple examples, isolate shared components, and assign a stable code to each word - a frequent task in reasoning sections of competitive exams.
This pattern is important because it trains systematic comparison and elimination: when multiple coded phrases share words, overlaps reveal each word's contribution to the code.
Pattern: Common Code for Multiple Words
Pattern
The key concept is: each distinct word (or token) in the phrase is represented by a consistent sub-code (letter, number, symbol, or block). By comparing several coded phrases that share words, you can isolate which sub-code corresponds to which word using intersection and difference logic.
Essentials to check every time:
- Find common words across coded phrases: identical sub-codes appearing in overlapping phrases usually map to the shared word.
- Use set-difference: subtract the sub-codes of overlapping phrases to reveal the code(s) for differing words.
- Watch position vs token: codes may be positional (first word → first token) or token-based (word → token anywhere); verify by checking different sentence orders.
- Account for multi-word tokens: some codes may represent word-pairs (e.g., "and the") - test with more examples to confirm.
- Confirm consistency: once you assign a code, check it against all examples to avoid accidental mis-assignment.
Step-by-Step Example
Question
In a certain code:
"Sky is blue" = 243
"Blue and sea" = 351
"Sea is sky" = ?
Solution
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Step 1: List codes and words
Phrase A: Sky is blue → 2 4 3.
Phrase B: Blue and sea → 3 5 1. -
Step 2: Identify the unambiguous common mapping
The word blue appears in both phrases A and B and is mapped to the common numeric token 3. So we assign blue = 3.
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Step 3: Use set-difference to map remaining words
A - B = {2,4,3} - {3,5,1} = {2,4} → these map to {sky, is}.
B - A = {3,5,1} - {2,4,3} = {5,1} → these map to {and, sea}.
Since 3 is already blue, the unique tokens left in A are 2 and 4; the unique tokens left in B are 5 and 1. The only consistent one-to-one mapping that assigns distinct tokens to distinct words is:- sky = 2
- is = 4
- blue = 3
- and = 5
- sea = 1
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Step 4: Apply mapping to the target phrase
"Sea is sky" → sea (1), is (4), sky (2) → 1 4 2.
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Final Answer:
142
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Quick Check:
Verify mapping against originals:
Sky is blue → 2 4 3 (matches).
Blue and sea → 3 5 1 (matches).
All words have unique tokens and no contradictions remain.
Quick Variations
1. Position-specific codes: each word position (1st/2nd/3rd) maps to a code regardless of the word order.
2. Token-based codes: each distinct word maps to its own sub-code (preferred unless position-specificity is shown).
3. Composite tokens: a code block may represent a pair or phrase (e.g., "and the").
4. Symbol mixing: codes may mix letters and numbers for different parts of the phrase.
5. Ambiguous functional words: small words (is, and, the) may reuse codes - more examples are required to disambiguate.
Trick to Always Use
- Step 1: Make a table of phrases vs code tokens and mark overlaps.
- Step 2: Use set-difference (A - B) to isolate the code for differing word(s).
- Step 3: Prefer token-based mapping over position-based unless the data forces a positional interpretation.
- Step 4: Verify each proposed mapping against all examples - a single contradiction means re-evaluate.
Summary
Summary
- Compare coded phrases to find overlapping numeric tokens that reveal shared words.
- Use set differences to isolate codes for unique words.
- Determine if the logic is token-based or position-based by comparing different sentence orders.
- Verify all mappings against every phrase to confirm consistency.
Example to remember:
“Sky is blue” = 243, “Blue and sea” = 351 ⇒ “Sea is sky” = 142
Hint: Find the common word first; that reveals a fixed numeric token.
Common Mistakes: Assuming position-based mapping instead of token-based mapping.