Solving the Coding Decoding Puzzle

This question is a classic example of a coding-decoding puzzle where a word is converted into a numerical value based on a specific rule or pattern. We are given two examples: 'PDU' is coded as '40', and 'HXO' is coded as '34'. We need to find the code for 'BMW' using the same rule.

Identifying the Coding Decoding Logic

Let's analyze the relationship between the letters in the words and the given numbers. A common approach in such problems is to use the alphabetical position of the letters.

• The standard alphabetical position assigns A=1, B=2, ..., Z=26.
• The reverse alphabetical position assigns A=26, B=25, ..., Z=1.

Let's test the standard alphabetical positions for 'PDU':

• P is the 16th letter.
• D is the 4th letter.
• U is the 21st letter.

Sum of standard positions = \(16 + 4 + 21 = 41\). This is close to 40, maybe \(41 - 1 = 40\)?

Let's test this potential rule (\(Sum - 1\)) on 'HXO' using standard positions:

• H is the 8th letter.
• X is the 24th letter.
• O is the 15th letter.

Sum of standard positions = \(8 + 24 + 15 = 47\). Applying the rule \(47 - 1 = 46\). This does not match the given code '34'. So, the standard alphabetical position rule is not correct.

Applying the Reverse Alphabetical Position

Let's try the reverse alphabetical position. The reverse position of a letter is calculated as \(27 - (\text{standard position})\).

• A = \(27 - 1 = 26\)
• B = \(27 - 2 = 25\)
• ...
• Z = \(27 - 26 = 1\)

Let's apply this to 'PDU':

• P is 16th standard position, so its reverse position is \(27 - 16 = 11\).
• D is 4th standard position, so its reverse position is \(27 - 4 = 23\).
• U is 21st standard position, so its reverse position is \(27 - 21 = 6\).

Sum of reverse positions for 'PDU' = \(11 + 23 + 6 = 40\). This matches the given code for 'PDU'.

Now let's apply this rule to 'HXO':

• H is 8th standard position, so its reverse position is \(27 - 8 = 19\).
• X is 24th standard position, so its reverse position is \(27 - 24 = 3\).
• O is 15th standard position, so its reverse position is \(27 - 15 = 12\).

Sum of reverse positions for 'HXO' = \(19 + 3 + 12 = 34\). This matches the given code for 'HXO'.

The pattern is clear: the code for a word is the sum of the reverse alphabetical positions of its letters.

Finding the Code for BMW

Now we apply the same rule to find the code for 'BMW':

• B is 2nd standard position, so its reverse position is \(27 - 2 = 25\).
• M is 13th standard position, so its reverse position is \(27 - 13 = 14\).
• W is 23rd standard position, so its reverse position is \(27 - 23 = 4\).

Sum of reverse positions for 'BMW' = \(25 + 14 + 4 = 43\).

Therefore, 'BMW' will be written as '43' in the same code language.

Summary of the Coding Decoding Pattern

The pattern observed is to calculate the reverse alphabetical position for each letter in the word and then sum these values to get the numerical code.

Revision Table: Key Coding Decoding Concepts

Understanding alphabetical positions is crucial for solving many coding decoding problems.

Additional Information on Coding Decoding

Coding decoding questions test your logical reasoning and pattern recognition skills. Besides using alphabetical positions, other common patterns include:

• Adding or subtracting a constant value to the position.
• Multiplying or dividing the position by a number.
• Using the sum or product of positions.
• Using the positions of opposite letters (as seen in this problem).
• Interchanging letters within the word.
• Applying rules based on vowels and consonants.
• Combining numerical and alphabetical codes.

Solving more coding decoding examples will help you become familiar with these various patterns.