1. You have a 3-gallon jug and a 5-gallon jug, and your goal is to measure out exactly 4 gallons of water. How do you do it?

a) Fill the 5-gallon jug, then use it to fill the 3-gallon jug.
b) Fill the 3-gallon jug, then use it to fill the 5-gallon jug.
c) Fill both jugs to the top and pour them into a larger container.
d) It's not possible to measure exactly 4 gallons.

2. You are given a set of scales and 12 identical-looking balls. One of the balls is slightly heavier than the others. How can you find the heavier ball using the scales only three times?

a) Weigh three groups of four balls each.
b) Weigh two groups of six balls each.
c) Weigh three groups of three balls each.
d) It's not possible to find the heavier ball in three weighings.

3. You have a 9x9 Sudoku grid. Each row, column, and subgrid must contain the numbers 1 through 9 without repetition. How do you solve the Sudoku puzzle?

a) Fill in the numbers randomly.
b) Use a process of elimination and logic to fill in the numbers.
c) Fill in the numbers sequentially from 1 to 9.
d) Guess the numbers until the puzzle is complete.

4. You have eight balls, and one is slightly heavier than the others. You also have a balance scale. What is the minimum number of weighings needed to find the heavier ball?

a) One weighing.
b) Two weighings.
c) Three weighings.
d) Four weighings.

5. You are in a room with three light switches, each controlling a different light bulb in the next room. How can you determine which switch corresponds to which bulb, if you are only allowed to enter the next room once?

a) Turn on all three switches and enter the room.
b) Turn on one switch, wait for a few minutes, turn it off, and then repeat with the other switches.
c) Turn on one switch, enter the room, and check the bulbs.
d) Flip the switches randomly and enter the room.

6. You have a rope that takes exactly one hour to burn from end to end. The rope does not burn at a consistent rate. How can you use the rope to measure exactly 45 minutes?

a) Light the rope at one end and wait for 45 minutes.
b) Light both ends of the rope simultaneously.
c) Cut the rope in half and burn one half.
d) Use a stopwatch to time the burning of the rope.

7. You have 12 marbles that appear identical, but one is slightly heavier than the others. How can you find the heavier marble using a balance scale in only three weighings?

a) Weigh two groups of six marbles each.
b) Weigh three groups of four marbles each.
c) Weigh four groups of three marbles each.
d) It's not possible to find the heavier marble in three weighings.

8. You have a 5-liter jug and a 3-liter jug, and your goal is to measure out exactly 4 liters of water. How do you do it?

a) Fill the 5-liter jug and pour it into the 3-liter jug.
b) Fill the 3-liter jug and pour it into the 5-liter jug.
c) Fill both jugs to the top and pour them into a larger container.
d) It's not possible to measure exactly 4 liters.

9. You have a 7-minute hourglass and an 11-minute hourglass. How can you measure exactly 15 minutes?

a) Start both hourglasses at the same time.
b) Start the 11-minute hourglass and flip it when it runs out, then start the 7-minute hourglass.
c) Start the 7-minute hourglass and flip it when it runs out, then start the 11-minute hourglass.
d) It's not possible to measure exactly 15 minutes.

10. You have a 4x4 grid with some cells filled with numbers from 1 to 4. Each row and each column must contain each number exactly once. How do you complete the grid?

a) Fill in the numbers randomly.
b) Use a process of elimination and logic to fill in the numbers.
c) Fill in the numbers sequentially from 1 to 4.
d) Guess the numbers until the grid is complete.