Subjects geometry

Symmetry Pattern A89839

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1. The problem asks to find 5 squares shaded on a 3x3 grid numbered 1 to 9 such that the pattern has 4 lines of symmetry. 2. The 4 lines of symmetry in a square grid are: vertical, horizontal, and the two diagonals. 3. For a pattern to have all 4 lines of symmetry, it must be symmetric about the center square (5). 4. Since exactly 5 squares are shaded, and the center square (5) must be shaded to maintain symmetry, we have 4 more squares to shade. 5. The 4 remaining shaded squares must be placed symmetrically in pairs across all lines of symmetry. 6. The only way to do this is to shade the center (5) and the four corner squares (1, 3, 7, 9), because corners are symmetric across all lines. 7. Thus, the shaded squares are 1, 3, 5, 7, 9. Final answer: 1,3,5,7,9