Understanding the Code Language Problem

This is a classic coding and decoding problem where words are assigned unique numerical codes. We are given four words and their corresponding codes in a specific code language. Our goal is to figure out the pattern or rule used for coding and then apply it to find the code for the word 'BTO'. The pattern in such problems is often a substitution, where each letter is assigned a specific digit. The digits forming the code for a word are then derived from the letters in that word.

Analyzing the Given Codes

We have the following pairs of words and codes:

• BOLT is coded as 2965
• DOLE is coded as 5723
• TADY is coded as 0368
• MASB is coded as 4819

The number of digits in the code for each word is equal to the number of letters in the word (four letters, four digits). This suggests a letter-to-digit mapping. However, observing the codes (e.g., BOLT 2965, DOLE 5723), the position of a letter doesn't necessarily correspond to the position of its digit in the code (e.g., 'O' is the second letter in BOLT and DOLE, but the second digits are 9 and 7 respectively). This indicates that the code is likely based on a direct substitution for each letter, and the digits for a word are simply a rearrangement of the codes for its individual letters.

Deducing Individual Letter Codes

Let's identify letters common across words and see if they share any digits in their codes. This helps us find the unique code for each letter.

• Compare BOLT ({B, O, L, T} → {2, 9, 6, 5}) and TADY ({T, A, D, Y} → {0, 3, 6, 8}). The common letter is 'T'. The common digit in their codes is 6. Conclusion: T ↔ 6
• Compare BOLT ({B, O, L, T} → {2, 9, 6, 5}) and MASB ({M, A, S, B} → {4, 8, 1, 9}). The common letter is 'B'. The common digit in their codes is 9. Conclusion: B ↔ 9
• Compare DOLE ({D, O, L, E} → {5, 7, 2, 3}) and TADY ({T, A, D, Y} → {0, 3, 6, 8}). Common letters are D. Common digits are {5, 7, 2, 3} and {0, 3, 6, 8}. The common digit is 3. Conclusion: D ↔ 3
• Compare TADY ({T, A, D, Y} → {0, 3, 6, 8}) and MASB ({M, A, S, B} → {4, 8, 1, 9}). Common letter is 'A'. We know T=6 and B=9. So {A, D, Y} ↔ {0, 3, 8} and {M, A, S} ↔ {4, 8, 1}. The common letter 'A' has a common digit 8. Conclusion: A ↔ 8

Now let's use the confirmed mappings to deduce others:

• From TADY ({T, A, D, Y} → {0, 3, 6, 8}), we know T=6, A=8, D=3. The remaining letter is Y and remaining digit is 0. Conclusion: Y ↔ 0
• From DOLE ({D, O, L, E} → {5, 7, 2, 3}), we know D=3. From previous comparisons, we also know {O, L} ↔ {5, 2}. So, {D, O, L, E} → {3, {O, L}, E} → {5, 7, 2, 3}. The digits for {O, L, E} are {5, 7, 2}. Since {O, L} correspond to {5, 2}, the remaining letter E must correspond to the remaining digit 7. Conclusion: E ↔ 7
• We still have {O, L} corresponding to {5, 2}. We need to figure out which one is O and which one is L.

Confirming Ambiguous Mappings and Finding the Code for BTO

We need the code for 'BTO'. We have already found the codes for B and T:

• B = 9
• T = 6
• O = ? (either 5 or 2)

The code for BTO will be formed by the digits for B, T, and O. The digits must be 9, 6, and either 5 or 2. Let's look at the options provided:

• Option 1: 962. Digits are {9, 6, 2}.
• Option 2: 865. Digits are {8, 6, 5}.
• Option 3: 482. Digits are {4, 8, 2}.
• Option 4: 958. Digits are {9, 5, 8}.

Only Option 1 (962) contains the digits 9 and 6 along with one of the possible digits for O (which is 2). This strongly suggests that the code for O is 2.

If O ↔ 2, then from {O, L} ↔ {5, 2}, it follows that L ↔ 5.

Let's verify these mappings with the original words:

• BOLT ({B, O, L, T}) → {9, 2, 5, 6}. The digits in 2965 are {2, 9, 6, 5}. Matches.
• DOLE ({D, O, L, E}) → {3, 2, 5, 7}. The digits in 5723 are {5, 7, 2, 3}. Matches.
• TADY ({T, A, D, Y}) → {6, 8, 3, 0}. The digits in 0368 are {0, 3, 6, 8}. Matches.
• MASB ({M, A, S, B}). We know B=9, A=8. {M, S} ↔ {4, 1}. This mapping is not uniquely determined but is consistent with 4819.

Final Letter-to-Digit Mapping (Relevant Letters)

Calculating the Code for 'BTO'

The word 'BTO' consists of the letters B, T, and O. Using our confirmed mapping:

• B corresponds to 9
• T corresponds to 6
• O corresponds to 2

The code for BTO is formed by the digits 9, 6, and 2. The order in the options suggests the code is simply the concatenation of the digits for the letters in order.

Code for BTO = Code for B + Code for T + Code for O

Conclusion

Based on the deduced letter-to-digit mapping from the given codes, the code for 'BTO' is 962.

Revision Table: Key Code Decoding Concepts

Additional Information: Practice Coding-Decoding Strategies

Solving coding and decoding problems for competitive exams requires keen observation and systematic analysis. Here are some tips:

• Always write down the given word-code pairs clearly.
• Look for common letters across different words.
• Check if common letters correspond to common digits or symbols in their codes. This is key for substitution codes.
• If direct commonality isn't obvious, check if the *set* of letters in a word corresponds to the *set* of digits/symbols in its code, regardless of position.
• Once a few mappings are found, use them to deduce the codes for remaining letters through elimination.
• Pay attention to the type of pattern: is it simple substitution, is position important, is it based on letter value (like A=1, B=2)?
• Practice with various types of coding problems to recognize patterns quickly.