Understanding the Coding Language Pattern

This coding language problem requires us to identify the specific rule used to convert letters into numbers. We are given two examples:

• 'MODERN' is coded as '4681095'
• 'TRACT' is coded as '29262'

Let's examine the letters and their corresponding codes:

For 'MODERN':

• M → 4
• O → 6
• D → 8
• E → 10
• R → 9
• N → 5

For 'TRACT':

• T → 2
• R → 9
• A → 2
• C → 6
• T → 2

We notice that the letter 'R' is coded as '9' in both words, and 'T' is coded as '2' in 'TRACT'. Also, 'O' is coded as '6' in 'MODERN', and 'C' is coded as '6' in 'TRACT'. This suggests that the coding might be based on the letter itself, possibly related to its position in the alphabet.

Identifying the Specific Coding Rule

Let's consider the alphabetical position of each letter (A=1, B=2, ..., Z=26) and see if there's a mathematical relationship with the given codes.

For 'MODERN':

• M is the 13th letter. Code is 4. \(13 \rightarrow 4\). Sum of digits \(1+3 = 4\).
• O is the 15th letter. Code is 6. \(15 \rightarrow 6\). Sum of digits \(1+5 = 6\).
• D is the 4th letter. Code is 8. \(4 \rightarrow 8\). Multiply by two \(4 \times 2 = 8\).
• E is the 5th letter. Code is 10. \(5 \rightarrow 10\). Multiply by two \(5 \times 2 = 10\).
• R is the 18th letter. Code is 9. \(18 \rightarrow 9\). Sum of digits \(1+8 = 9\).
• N is the 14th letter. Code is 5. \(14 \rightarrow 5\). Sum of digits \(1+4 = 5\).

For 'TRACT':

• T is the 20th letter. Code is 2. \(20 \rightarrow 2\). Sum of digits \(2+0 = 2\).
• R is the 18th letter. Code is 9. \(18 \rightarrow 9\). Sum of digits \(1+8 = 9\).
• A is the 1st letter. Code is 2. \(1 \rightarrow 2\). Multiply by two \(1 \times 2 = 2\).
• C is the 3rd letter. Code is 6. \(3 \rightarrow 6\). Multiply by two \(3 \times 2 = 6\).
• T is the 20th letter. Code is 2. \(20 \rightarrow 2\). Sum of digits \(2+0 = 2\).

Based on these observations, the rule appears to be:

• If the alphabetical position of a letter is a single digit (1 to 9), multiply the position by 2.
• If the alphabetical position of a letter is a double digit (10 to 26), sum the digits of the position.

Applying the Coding Rule to BELGIUM

Now, let's apply this rule to the word 'BELGIUM' to find its code.

Concatenating the encoded values for each letter of 'BELGIUM', we get: 4103141834.

Conclusion

Following the identified coding pattern, the word 'BELGIUM' is coded as '4103141834'.

Revision Table: Coding Language Rules

Additional Information: Pattern Recognition in Coding Problems

Coding-decoding problems in logical reasoning often involve identifying a consistent pattern or rule applied to transform a set of letters or words into another form (numbers, symbols, other letters). Common patterns include:

• Using alphabetical positions (forward or reverse).
• Adding, subtracting, multiplying, or dividing positions.
• Summing or manipulating digits of the position.
• Skipping a fixed number of letters.
• Reversing the order of letters or groups of letters.
• Using codes based on a fixed code-table for specific letters.
• Combining multiple rules.

Solving these problems requires careful observation, comparing the given examples, forming hypotheses about the rule, and testing the hypotheses against all provided examples before applying the rule to the word that needs to be coded or decoded. Paying attention to repeating letters and their codes is often a key starting point.