Solving the Letter-to-Number Coding Language Puzzle

This question asks us to decipher a coding language where words are converted into numbers based on a specific rule. We are given two examples: 'PLACE' coded as 5311216 and 'PLAY' coded as 2511216. We need to use these examples to find the coding rule and apply it to the word 'RATE'.

Analyzing the Given Examples

Let's look at the words and their corresponding codes:

• PLACE (5 letters) → 5311216 (7 digits)
• PLAY (4 letters) → 2511216 (7 digits)

The number of digits in the code is more than the number of letters, suggesting that each letter might correspond to one or more digits. Let's consider the position of each letter in the English alphabet (A=1, B=2, ..., Z=26).

Letters and their Alphabetic Positions:

• P: 16
• L: 12
• A: 1
• C: 3
• E: 5
• Y: 25
• R: 18
• T: 20

Now let's see if the digits in the code relate to these positions. Comparing the two codes, 5311216 and 2511216, we notice that the last six digits (311216 and 511216) are very similar, only the first digit is different.

Let's try mapping the letters of 'PLACE' to the digits 5311216:

• P (16)
• L (12)
• A (1)
• C (3)
• E (5)

If we look at the digits 5, 3, 1, 1, 2, 1, 6, they seem to correspond to the letter values, possibly split for two-digit numbers. Let's test if the letters in reverse order match the concatenated digits:

• E (5) → 5
• C (3) → 3
• A (1) → 1
• L (12) → 1, 2
• P (16) → 1, 6

Concatenating these digits in the order E, C, A, L, P gives us: 5 | 3 | 1 | 12 | 16 which becomes 5311216. This matches the code for 'PLACE'.

Identifying the Coding Rule

Based on the analysis of 'PLACE', the rule appears to be:

1. Take the letters of the word in reverse order.
2. For each letter, find its position in the alphabet (A=1, Z=26).
3. If the position is a single digit (1-9), use that digit.
4. If the position is a two-digit number (10-26), use both digits separately.
5. Concatenate all the obtained digits in the order of the reversed letters.

Verifying the Rule with 'PLAY'

Let's apply this rule to the word 'PLAY':

1. Reverse order of letters: Y, A, L, P
2. Alphabetic positions:
   • Y: 25
   • A: 1
   • L: 12
   • P: 16
3. Digits from positions:
   • Y (25) → 2, 5
   • A (1) → 1
   • L (12) → 1, 2
   • P (16) → 1, 6
4. Concatenate the digits: 2 | 5 | 1 | 1 | 2 | 1 | 6

Joining the digits gives 2511216. This matches the given code for 'PLAY'. The rule is confirmed.

Applying the Rule to 'RATE'

Now, let's apply the same coding rule to the word 'RATE':

1. Reverse order of letters: E, T, A, R
2. Alphabetic positions:
   • E: 5
   • T: 20
   • A: 1
   • R: 18
3. Digits from positions:
   • E (5) → 5
   • T (20) → 2, 0
   • A (1) → 1
   • R (18) → 1, 8
4. Concatenate the digits: 5 | 2 | 0 | 1 | 1 | 8

Joining the digits gives the code 520118.

Comparing with Options

The code for 'RATE' is 520118.

Let's check the given options:

• Option 1: 520118
• Option 2: 511207
• Option 3: 519128
• Option 4: 420116

Our calculated code, 520118, matches Option 1.

Conclusion

Following the established coding rule, the word 'RATE' is coded as 520118.

Revision Table: Coding Rule Summary

Additional Information: Letter Coding Techniques

Coding-decoding questions often involve mapping letters to numbers or other letters based on specific rules. Common techniques include:

• Alphabetic Position: Using the serial number of a letter (A=1, Z=26).
• Reverse Alphabetic Position: Using position from the end of the alphabet (A=26, Z=1).
• Adding/Subtracting a Constant: Shifting letter positions by a fixed number.
• Sum of Positions: Combining the position values of letters in a word (e.g., summing them up).
• Pattern-Based Mapping: More complex rules like the one in this problem (reverse order, splitting digits, etc.), vowel/consonant rules, or pairs of opposite letters (A-Z, B-Y, etc.).
• Substitution: Replacing one letter with another letter or symbol based on a pattern.

Practicing different types of coding and decoding puzzles helps in quickly identifying the logic during exams.