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Let's break down the questions one by one and work through the solutions.

### 1. **Bookworm Problem:**
   The bookworm travels horizontally from the first page of Volume I to the last page of Volume III. The total thickness of each book is 1 inch, and the covers of the books are 1/8 inch thick. However, note that since the worm starts on the first page of Volume I and ends on the last page of Volume III, we only count the middle section of Volume II. Thus, the bookworm skips the first cover of Volume I and the last cover of Volume III.

   Calculation:
   - Distance through Volume I and Volume III covers = 2 covers × 1/8 inch = 1/4 inch.
   - Middle volume (Volume II) = 1 inch.
   
   Total distance:  
   \[
   1 + \frac{1}{4} = 1.25 \, \text{inches}
   \]

   So, the bookworm travels **1.25 inches**.

### 2. **Nine Dots Problem (Four Lines Puzzle):**
   The objective is to connect all nine dots using exactly four straight lines without lifting the pencil from the paper. This is a famous problem that involves thinking "outside the box." The solution requires you to extend the lines beyond the grid's boundary.

   Here’s how it works:
   - Start at one corner, move diagonally outwards, and extend the line.
   - You will need to draw the lines beyond the confines of the grid.

   If you'd like, I can provide a more detailed diagram demonstrating the solution.

### 3. **KenKen Puzzle:**
   To solve the KenKen puzzle, the goal is to fill in each cell with numbers such that no number repeats in any row or column, and the numbers must satisfy the arithmetic operations within each outlined group of cells.

   I'll need to analyze the puzzle grid more closely to provide the correct values.

### 4. **Magician's Number Trick:**
   Let the initial number chosen by the audience member be \( x \).

   The magician gives the following instructions:
   1. Add 15 to the number: \( x + 15 \)
   2. Multiply the result by 3: \( 3(x + 15) = 3x + 45 \)
   3. Subtract 9: \( 3x + 45 - 9 = 3x + 36 \)
   4. Divide the result by 3: \( \frac{3x + 36}{3} = x + 12 \)

   The result is always \( x + 12 \). So when the volunteer says 32, the magician subtracts 12 to find the original number:
   \[
   32 - 12 = 20
   \]

   Therefore, the volunteer's original number was **20**.

### 5. **Cryptarithmetic Problem (ABC × B = EDC):**
   This cryptarithmetic puzzle requires assigning digits to the letters such that the multiplication holds. Here, we need to solve \( ABC \times B = EDC \). The values for each letter will need a more detailed solution approach, which often involves trial and error or a systematic search. I can work on the solution if you’d like.

### 6. **Missionaries and Cannibals Puzzle:**
   The objective is to safely transfer three missionaries and three cannibals across a river using a boat that can carry at most two people. The condition is that at no point can the cannibals outnumber the missionaries on either side.

   The minimum number of trips required for this puzzle is **11**. If you'd like, I can provide a detailed step-by-step explanation of the solution.

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Would you like a detailed explanation for any of these solutions? Let me know if you'd like me to elaborate or clarify any part.

### Follow-up Questions:
1. How can we represent the bookworm problem visually?
2. What is the logic behind solving the KenKen puzzle?
3. Can you explain how extending the lines solves the nine dots puzzle?
4. What strategy can be used to systematically solve cryptarithmetic problems?
5. Why is the number of trips in the Missionaries and Cannibals problem minimized to 11?

### Tip:
In KenKen puzzles, always focus on the operations and ensure that no number repeats in any row or column, just like Sudoku.

Solve the following problems:
1. Three volumes of a series of books are on a shelf with no space in between. Each volume is 1 inch thick without its covers. Each cover is 1/8 inch thick. A bookworm bores horizontally from the first page of volume I to the last page of volume III. How far does the bookworm travel?
2. Nine dots are arranged as shown. Is it possible to connect the nine dots with exactly four lines if you are not allowed to remove your pencil from the paper?
3. Solve the given KenKen puzzle.
4. A magician asked someone to volunteer from the audience and instructed them to follow a series of mathematical operations, eventually determining their original number. How did the magician do it?
5. Identify the value of each letter in the cryptarithmetic problem ABC x B = EDC.
6. Three missionaries and three cannibals need to cross a river in a boat that can only carry two people. How should they cross the river in the minimum number of trips?

Discover solutions to intriguing math puzzles like the Bookworm problem, Nine Dots puzzle, KenKen, magician's trick, and cryptarithmetic problem. Suitable for students in Grades 6-9.

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