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?

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

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

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?

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?

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?

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

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?

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

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?