Solving the Code Language Puzzle: Finding the Code for M

This question asks us to decipher a code language where words are represented by sequences of digits. We are given two examples of coded words:

• 'MOST' is coded as '3472'
• 'STOW' is coded as '2634'

Our goal is to find the specific digit that codes the letter 'M'.

Analyzing the Given Coded Words

In code language problems like this, each letter usually corresponds to a unique digit. The sequence of digits in the code typically matches the sequence of letters in the word. However, sometimes there are variations. Let's look at the letters and the digits used in the given examples.

Identifying Common and Unique Elements

Let's compare the letters present in both words and the digits present in both codes:

• Letters in both words: S, T, O
• Digits in both codes: 2, 3, 4

This tells us that the letters S, T, and O are coded using the digits 2, 3, and 4. We don't know which letter maps to which digit yet, but we know these sets correspond to each other.

Now, let's look at the letters and digits that are unique to each example:

• Letter unique to 'MOST': M (It appears in 'MOST' but not in 'STOW')
• Digit unique to '3472': 7 (It appears in '3472' but not in '2634'. Digits 2, 3, and 4 are common)

Similarly:

• Letter unique to 'STOW': W (It appears in 'STOW' but not in 'MOST')
• Digit unique to '2634': 6 (It appears in '2634' but not in '3472'. Digits 2, 3, and 4 are common)

Deducing the Code for 'M'

Since 'M' is the letter unique to the word 'MOST', and '7' is the digit unique to the code '3472', it is highly likely that the letter 'M' is coded as the digit '7'. This approach relies on the principle that unique elements in the input (the word) correspond to unique elements in the output (the code) in such puzzles, especially when common elements help establish the rest of the mapping.

Based on this logic:

• 'M' is coded as '7'
• 'W' is coded as '6'
• The letters 'S', 'T', and 'O' are coded using the digits '2', '3', and '4' (though we don't need to find their exact mapping to answer the question).

Verification (Optional but Recommended)

Let's quickly see if this fits with the given codes. If M=7 and W=6, then:

• For 'MOST' (3472), the digits are {3, 4, 7, 2}. This set includes our code for M (7). The remaining digits {3, 4, 2} are for {O, S, T}.
• For 'STOW' (2634), the digits are {2, 6, 3, 4}. This set includes our code for W (6). The remaining digits {2, 3, 4} are for {S, T, O}.

This confirms that the sets of codes align with the letters based on our deduction.

Conclusion

By comparing the letters and digits in the two examples and identifying the unique elements, we found that the letter 'M' corresponds to the digit '7'.

The code for 'M' is 7.

Revision Table: Code Language Mapping

Additional Information on Coding-Decoding

Coding-Decoding is a common type of question in logic and reasoning sections of competitive exams. These questions test your ability to identify patterns in how letters, words, or numbers are transformed into a coded format. Common types of coding include:

• Letter Coding: Letters are replaced by other letters based on a pattern (e.g., shifting positions in the alphabet).
• Number/Symbol Coding: Letters or words are replaced by numbers or symbols. The pattern can be direct substitution (as seen in this problem), positional value, or based on arithmetic operations.
• Mixed Coding: Sentences are coded, and you need to find the code for a specific word by comparing different sentences.

In substitution codes like this one, the key is often to look for common elements across different coded examples or for elements that are unique to a single example to break the code.