# Puzzle Games: Breaking Thought Patterns

1. There are three switches in a room, each controlling a light in three different rooms. You can only enter the room once. How do you determine which switch controls which light?

Correct Answer:Turn on the first switch, wait for a while, and then turn it off. Then turn on the second switch and quickly enter the room. The room with the light on corresponds to the first switch, the room with the light off corresponds to the second switch, and the last room corresponds to the third switch.

2. A farm has chickens and rabbits, totaling 35 animals and 94 legs. How many of each animal are there?

Correct Answer:Solve the following system of equations:
x + y = 35
2x + 4y = 94
where x represents the number of chickens and y represents the number of rabbits. This yields x=23 and y=12.

3. You have a 3-liter and a 5-liter jug. How can you accurately measure 4 liters of water?

Correct Answer:First fill the 5-liter jug and pour 3 liters into the 3-liter jug, leaving 2 liters in the 5-liter jug. Then empty the 3-liter jug, pour the 2 liters from the 5-liter jug into the 3-liter jug, and fill the 5-liter jug again. Now pour water from the 5-liter jug into the 3-liter jug until it is full. This leaves 4 liters in the 5-liter jug.

4. There are two piles of stones, each with 10 stones. One pile is all fake, and the other is all real. You have a scale but can only use it once. How can you find the pile of real stones?

Correct Answer: Take one stone from the first pile and add it to the second pile. Then weigh the piles:
– If the weights are the same, the stone taken is real.
– If the weights are different, the heavier pile contains the real stones.

5. A person is on top of a 100-story building with two identical glass balls. If a ball doesn’t break when dropped from the 100th floor, it won’t break when dropped from the 99th floor either. How can you find the critical floor using the fewest drops?

Correct Answer:This is a classic binary search problem. Approach it by dividing the problem into halves, starting at the 50th floor, and proceeding based on whether the ball breaks or not.

6.There is a 3×3 grid with one chess piece in each square. You can choose any row or column and remove all the pieces from it. What is the minimum number of pieces you need to remove to ensure that no row or column has any pieces left?

Correct Answer:You only need to remove 4 pieces, the four pieces in the middle of the grid.

7. A piece of paper is 0.1 millimeters thick. If you fold it in half 50 times, how thick will it be?

Correct Answer:Folding the paper doubles its thickness each time, so after 50 folds, the thickness will be  millimeters.

8. A chessboard has 8×8 squares, and there are 32 grains of wheat on it. If you start by placing one grain in the first square, then two in the second, and continue doubling the number of grains for each subsequent square, on which day will the total number of grains exceed 100 million?

Correct Answer:The total number of grains on the nth day is 2^n – 1. Solving 2^n – 1 > 10^8 gives n > log_2(10^8 + 1), so the total will exceed 100 million on the 27th day.

9. You have a 4-liter jug and a 9-liter jug. How can you measure exactly 6 liters of water?

Correct Answer:Fill the 9-liter jug and pour it into the 4-liter jug, leaving 5 liters in the 9-liter jug. Then empty the 4-liter jug, pour the 5 liters from the 9-liter jug into the 4-liter jug.

10. A bridge can only hold the weight of two people at a time. Four people need to cross, and their individual crossing times are 1, 2, 5, and 10 minutes. What is the shortest time it takes for all of them to cross?

Correct Answer:Have the 1-minute and 2-minute cross together, then the 1-minute returns. Next, the 5-minute and 10-minute cross together, and the 2-minute returns. Finally, the 1-minute and 2-minute cross together.