Problem 11 · Symmetry · 3 points
Made by AI and not reviewed by a real person.
Nora’s 3-by-3 tile coaster has exactly five green tiles. Its colors look unchanged after she turns it halfway around (180°); which tile must be green?
- Top-left tile
- Top-middle tile
- Bottom-right tile
- Middle-left tile
- Center tile
Show a hint
- Draw a 3-by-3 grid and trace where each position moves in a half-turn. Use the unchanged color pattern to work out which positions must match.
- Tiles that trade places must have the same color. Think about how many green tiles those matching groups can contribute to the total of five.
Show the answer and solution
Answer: E — Center tile
A half-turn exchanges the eight outer tiles in four pairs and leaves the center tile in place. Each pair contains either zero or two green tiles, so the outer tiles contribute an even number of green tiles. Since the coaster has five green tiles, the center tile must be green. The top-left tile is not required to be green: the center, top-middle, bottom-middle, middle-left, and middle-right tiles could be the five green tiles, leaving the top-left tile white.