Question 1:

Alice, Bob, and Charlie are playing a game. Alice always tells the truth, Bob always lies, and Charlie sometimes tells the truth and sometimes lies. They made the following statements:

Alice: "Bob is lying."

Bob: "Charlie is lying."

Charlie: "Alice is lying."

Who is lying?

Explanation: If Alice is telling the truth, then Bob must be lying, which would make Charlie's statement true. However, this contradicts Charlie's statement. Therefore, Alice is lying.

Question 2:

You have a 3-liter jug and a 5-liter jug. How can you measure exactly 4 liters of water using only these two jugs?

Explanation: The correct method is described in option A. By carefully following the steps mentioned, you can measure exactly 4 liters of water using the 3-liter and 5-liter jugs.

Question 3:

There are five friends sitting in a row: Alex, Ben, Chris, David, and Eric. They have different heights. The following statements are true:

1. Alex is taller than Ben.

2. Chris is shorter than David.

3. Eric is taller than Ben.

Who is the shortest?

Explanation: From the given statements, we can determine the order of heights from shortest to tallest: Chris, Ben, Alex, David, Eric. Therefore, Chris is the shortest.

Question 4:

You have a 4x4 grid of squares. You want to color each square either red or blue, such that no two adjacent squares have the same color. What is the maximum number of squares you can color?

Explanation: To maximize the number of squares you can color, you can alternate the colors in a checkerboard pattern. In a 4x4 grid, this allows you to color 8 squares.

Question 5:

You are given a set of 12 coins, out of which one is fake and weighs less than the others. You have a balance scale, and you can use it three times. How can you identify the fake coin?

Explanation: The correct method is described in option A. By dividing the coins into groups and comparing them on the balance scale, you can identify the group of coins containing the fake coin. Then, by comparing two coins from that group, you can determine the lighter coin, which is the fake one.