Vectors Up

Objective

Hunt down 10 hidden vectors by asking strategic questions about polynomials and coordinates. Maximize your score by guessing with fewer questions!

How to Play

1. Choose Your Level (V: 1-3): Higher levels mean larger coordinate ranges for vectors.
   • Level 1: Coordinates between -10 and 10
   • Level 2: Coordinates between -30 and 30
   • Level 3: Coordinates between -100 and 100
2. Choose Polynomial Depth (D: 1-3): Maximum degree of polynomials you can use to constrain the search space.
3. Hunt 10 Vectors: For each round, you start with 21 points and have up to 20 questions to find the hidden vector.
4. Ask Strategic Questions:
   • "Is the vector above, below, or on this polynomial?" - Define a polynomial of degree ≤ D to split the search space
   • "Is the vector at this point?" - Make a direct guess at the coordinates
5. Track Your Progress: After each question, see the possible region (in green) where the vector could be.
6. Score Points: Each question costs 1 point. Find the vector faster to score higher! (21 - questions used)

Mathematical Concepts

Polynomial Constraints: Understanding how polynomials divide the coordinate plane into regions.

Binary Search Strategy: Using questions efficiently to narrow down possibilities.

Coordinate Geometry: Visualizing regions and constraints on the xy-plane.

Tips

• Start with simple polynomials to divide the space efficiently
• Linear polynomials (y = mx + b) are great for binary search
• Use the visual feedback to guide your next question
• Don't guess the exact point until you've narrowed it down!