Question

Given an input line of numbers and words, a machine rearranges them following a particular rule in each step. Using the illustrated pattern, find the position of $58$ in the \emph{fourth step for:} Input: \texttt{cb kb eb 58 49 23 38 jb nb gb 69 82}

• A. Second from the left
• B. Fourth from the right
• C. Third from the right
• D. Seventh from the left

Hint:

In step–arrangement problems, first decode the leftmost and rightmost placements per step; then simulate only as many steps as needed to locate the target element.

Answer 1

The Correct Option is C

Step 1: Infer the rule from the example.
At each step, the alphabetically smallest remaining word is placed at the extreme left, and the largest remaining number is placed at the extreme right. Repeating this gives all words first (ascending), then numbers (descending). Step 2: Order words and numbers for the new input.
Words (alphabetical): $cb, eb, gb, jb, kb, nb$.
Numbers (descending): $82, 69, 58, 49, 38, 23$. Step 3: Build the steps up to Step 4. \[ \begin{aligned} \text{Step 1: }& cb\; kb\; eb\; 58\; 49\; 23\; 38\; jb\; nb\; gb\; 69\; 82
\text{Step 2: }& cb\; eb\; kb\; 58\; 49\; 23\; 38\; jb\; nb\; gb\; 69\; 82
\text{Step 3: }& cb\; eb\; gb\; kb\; 49\; 23\; 38\; jb\; nb\; 82\; 69\; 58
\text{Step 4: }& cb\; eb\; gb\; jb\; kb\; 23\; 38\; nb\; 82\; 69\; 58\; 49 \end{aligned} \] Step 4: Locate $58$ in Step 4.
In Step 4 the tail is $82, 69, 58, 49$ (left to right). Hence $58$ is third from the right. \[ \boxed{\text{Third from the right}} \]