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ข้อความเดิมเขียนโดยคุณ Mobius

ต่อครับ



14. Squares on an infinite chessboard are being painted. As shown in the diagram below, three squares (lightly shaded) are initially painted. In the first step, we paint all squares (darkly shaded) which share at least one edge with squares already painted. The same rule applies in all subsequent steps. Find the number of painted squares after one hundred steps.

ผมคิดว่าตอบ 403 ครับ

4n-1

3+7+11+15+...+403

= 4(1)-1 + 4(2) -1 + 4(3) -1 + ... 4(101)-1

= 4(1+2+3+...101) - 101 = 20503

มีสีเทาที่ระบายอยู่ก่อน 3 รูป จึงมีทั้งหมด 20,503 -3 = 20,500 รูป