LPDP Scholarship Problem-Solving and Analytical Questions

1. A farmer has 17 sheep and all but 9 die. How many sheep are left?

2. You have a 5-liter jug and a 3-liter jug. How can you measure out exactly 4 liters using these jugs?

3. A man is pushing his car along a road when he comes to a hotel. He shouts, "I'm bankrupt!" Why?

4. You have a 12-liter container that is filled with a mixture of 1 part wine and 3 parts water. If you remove 3 liters of the mixture and replace it with 3 liters of pure wine, what is the new ratio of wine to water in the container?

5. In a certain city, the population doubles every 20 years. If the population is currently 100,000, how many years will it take for the population to reach 800,000?

6. A square and a circle have the same area. If the side of the square is 8 cm, what is the radius of the circle?

7. In a room, there are 9 people. Each person shakes hands with every other person exactly once. How many handshakes occur in total?

8. You have two ropes that each take an hour to burn, but they do not burn at a constant rate. How can you measure 45 minutes using these ropes?

9. A puzzle states that you have an 8x8 chessboard. You can remove two diagonally opposite corners. Can you cover the remaining board with 31 dominoes? Justify your answer.

10. Imagine you have a box with 10 red balls and 10 blue balls. You are blindfolded and asked to take out 10 balls. What is the minimum guaranteed number of a single color you can ensure you have?