87 Spatial Problem-Solving
Problem Solving
Spatial Reasoning
Practical Application
Geometric Thinking
Logical Deduction
87.1 Description:
This task involves using spatial reasoning to solve practical problems or puzzles. It evaluates the model’s ability to apply spatial concepts to real-world scenarios and find creative solutions.
87.2 Modality:
Text only
87.3 Examples:
87.3.1 Example 1:
Input:
You have a 10-liter jug and a 6-liter jug, and an unlimited supply of water. How can you measure exactly 4 liters of water?Output:
Here's how to measure exactly 4 liters:
1. Fill the 6-liter jug completely.
2. Pour water from the 6-liter jug into the 10-liter jug until it's full (which takes 6 liters).
3. The 6-liter jug now contains 0 liters, and the 10-liter jug contains 10 liters.
4. Pour water from the 10-liter jug back into the 6-liter jug until it's full.
5. The 10-liter jug now contains exactly 4 liters of water.87.3.2 Example 2:
Input:
You have a rectangular room that is 15 feet long and 10 feet wide. You want to place a circular rug in the center of the room, leaving at least 2 feet of space between the edge of the rug and the walls on all sides. What is the maximum diameter the rug can be?Output:
To find the maximum diameter of the rug:
1. Available space:
Length: 15 - (2 * 2) = 11 feet
Width: 10 - (2 * 2) = 6 feet
2. The rug must fit within both dimensions, so we use the smaller dimension (6 feet).
3. The maximum diameter of the rug is 6 feet.
This ensures the rug fits within the room while maintaining at least 2 feet of space from all walls.