ELECTROCARDIOGRAPH Word Transformation Analysis

This puzzle involves transforming the word "ELECTROCARDIOGRAPH" through a series of specific steps. We need to carefully follow each instruction to find the letter that ends up exactly in the middle of the final transformed word.

Original Word Details

The original word is "ELECTROCARDIOGRAPH". Let's count the letters:

E L E C T R O C A R D I O G R A P H

There are 18 letters in the original word.

Step-by-Step Transformation

We will perform the transformations in the exact order given:

Step 1: Reversing the First Half

The word has 18 letters. The first half consists of the first ${ \frac{18}{2} } = 9$ letters.

• First half: ELECTROCA
• Reversing these 9 letters gives: ACORTCELE
• The remaining part of the word is: RDIOGRAPH
• Combining the reversed first half with the remaining part results in the new arrangement: ACORTCELERDIOGRAPH

This intermediate word has 18 letters.

Step 2: Moving the Last but One Letter

We need to identify the last but one letter of the original word "ELECTROCARDIOGRAPH".

• Original word: ELECTROCARDIOGRAPH
• Last letter: H
• Last but one letter: P

This letter 'P' is then placed at the very beginning of the current arrangement:

• Current arrangement: ACORTCELERDIOGRAPH
• New arrangement after prepending 'P': PACORTCELERDIOGRAPH

This word now has $18 + 1 = 19$ letters.

Step 3: Adding 'S' at the End

Finally, the letter 'S' is added to the end of the current arrangement:

• Current arrangement: PACORTCELERDIOGRAPH
• Final transformed word: PACORTCELERDIOGRAPH S

The final word has $19 + 1 = 20$ letters.

Finding the Middle Letter

The final transformed word is "PACORTCELERDIOGRAPH S", which has 20 letters.

For a word with an even number of letters ($N$), there isn't a single letter exactly in the middle. Instead, there are two middle letters. These are located at positions $ \frac{N}{2} $ and $ \frac{N}{2} + 1 $.

In this case, $N=20$. The middle positions are:

• Position 1: $ \frac{20}{2} = 10 $
• Position 2: $ \frac{20}{2} + 1 = 11 $

Let's identify the letters at these positions in the final word:

P A C O R T C E L E R D I O G R A P H S

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

The 10th letter is 'E'. The 11th letter is 'R'.

Since the question asks for the letter "exactly in the middle" and 'R' is one of the two central letters and is provided as an option, 'R' is identified as the result.