Understanding the Coding Language Problem

This question asks us to decode a word based on a simple substitution pattern provided for other words. We are given specific numerical codes for 'WORD', 'GOD', and 'PUT'. Our goal is to use these examples to figure out the code for each letter and then apply that pattern to find the code for 'GOOD'. This type of problem tests our ability to find patterns and apply them consistently.

Analyzing the Given Codes and Letters

Let's look at the codes provided:

• 'WORD' is coded as '1234'
• 'GOD' is coded as '524'
• 'PUT' is coded as '678'

We need to find the code for 'GOOD'. Notice that some letters appear in more than one word, which is helpful for confirming the letter-to-number mapping.

Decoding the Letter-to-Number Mapping

From 'WORD' = '1234', we can initially assume:

• W = 1
• O = 2
• R = 3
• D = 4

Now let's look at 'GOD' = '524'. Comparing this to our initial assumption from 'WORD':

• 'G' must be 5.
• 'O' is 2 (this matches our assumption from 'WORD').
• 'D' is 4 (this matches our assumption from 'WORD').

The codes for 'O' and 'D' are consistent between 'WORD' and 'GOD'. This confirms our mapping for these letters.

Finally, let's check 'PUT' = '678'. The letters P, U, and T do not appear in the other two words, so this simply gives us the codes for these new letters:

• P = 6
• U = 7
• T = 8

Summary of the Code Mapping

Based on the analysis, the consistent mapping of letters to numbers is:

• G = 5
• O = 2
• R = 3
• D = 4
• W = 1
• P = 6
• U = 7
• T = 8

We can represent this mapping clearly in a table.

Coding the Word 'GOOD'

Now we need to find the code for the word 'GOOD'. We will use the letter-to-number mapping we just established. The word 'GOOD' consists of the letters G, O, O, and D.

• The code for G is 5.
• The code for O is 2.
• The code for the second O is also 2.
• The code for D is 4.

Putting these codes together in order gives us the code for 'GOOD'.

\text{G} \rightarrow 5

\text{O} \rightarrow 2

\text{O} \rightarrow 2

\text{D} \rightarrow 4

So, the code for 'GOOD' is 5224.

Verifying the Code

Let's check the options provided to see which one matches our decoded number for 'GOOD'. The calculated code is 5224.

• Option 1: 7224 (Does not match)
• Option 2: 6224 (Does not match)
• Option 3: 5224 (Matches!)
• Option 4: 4223 (Does not match)

The code 5224 matches Option 3.

Revision Table: Coding Language Mapping

Additional Information: Substitution Ciphers

The coding language used in this problem is a simple form of a substitution cipher. In a substitution cipher, each letter (or sometimes a group of letters) is replaced by another character, number, or symbol. This is one of the oldest methods of encryption.

• Simple Substitution: Each letter is consistently replaced by one other character throughout the message. This is what we saw in the problem. A well-known example is the Caesar cipher, where each letter is shifted a fixed number of positions down the alphabet.
• Polyalphabetic Substitution: The substitution pattern changes depending on the position of the letter in the message. The Vigenère cipher is an example of this.
• Frequency Analysis: Simple substitution ciphers can often be broken by analyzing the frequency of letters in the coded message, as certain letters (like 'E' in English) appear more often than others.

These coding language problems in reasoning tests are simplified versions that require careful observation and pattern recognition to decode the mapping.