一个正方形分成16个相等的正方形，问共有几个正方形？

Question

如果用数学的排列组合来回答有哪几种情况？

Answer 1

50个 斜的也要考虑的16个方块的是50个，25个方块的是107个
dot list ((1, 1), (1, 2), (2, 1), (2, 2))
dot list ((1, 1), (1, 3), (3, 1), (3, 3))
dot list ((1, 1), (1, 4), (4, 1), (4, 4))
dot list ((1, 1), (1, 5), (5, 1), (5, 5))
dot list ((1, 2), (1, 3), (2, 2), (2, 3))
dot list ((1, 2), (1, 4), (3, 2), (3, 4))
dot list ((1, 2), (1, 5), (4, 2), (4, 5))
dot list ((1, 2), (2, 1), (2, 3), (3, 2))
dot list ((1, 2), (2, 4), (3, 1), (4, 3))
dot list ((1, 2), (2, 5), (4, 1), (5, 4))
dot list ((1, 3), (1, 4), (2, 3), (2, 4))
dot list ((1, 3), (1, 5), (3, 3), (3, 5))
dot list ((1, 3), (2, 1), (3, 4), (4, 2))
dot list ((1, 3), (2, 2), (2, 4), (3, 3))
dot list ((1, 3), (2, 5), (3, 2), (4, 4))
dot list ((1, 3), (3, 1), (3, 5), (5, 3))
dot list ((1, 4), (1, 5), (2, 4), (2, 5))
dot list ((1, 4), (2, 1), (4, 5), (5, 2))
dot list ((1, 4), (2, 2), (3, 5), (4, 3))
dot list ((1, 4), (2, 3), (2, 5), (3, 4))
dot list ((2, 1), (2, 2), (3, 1), (3, 2))
dot list ((2, 1), (2, 3), (4, 1), (4, 3))
dot list ((2, 1), (2, 4), (5, 1), (5, 4))
dot list ((2, 2), (2, 3), (3, 2), (3, 3))
dot list ((2, 2), (2, 4), (4, 2), (4, 4))
dot list ((2, 2), (2, 5), (5, 2), (5, 5))
dot list ((2, 2), (3, 1), (3, 3), (4, 2))
dot list ((2, 2), (3, 4), (4, 1), (5, 3))
dot list ((2, 3), (2, 4), (3, 3), (3, 4))
dot list ((2, 3), (2, 5), (4, 3), (4, 5))
dot list ((2, 3), (3, 1), (4, 4), (5, 2))
dot list ((2, 3), (3, 2), (3, 4), (4, 3))
dot list ((2, 3), (3, 5), (4, 2), (5, 4))
dot list ((2, 4), (2, 5), (3, 4), (3, 5))
dot list ((2, 4), (3, 2), (4, 5), (5, 3))
dot list ((2, 4), (3, 3), (3, 5), (4, 4))
dot list ((3, 1), (3, 2), (4, 1), (4, 2))
dot list ((3, 1), (3, 3), (5, 1), (5, 3))
dot list ((3, 2), (3, 3), (4, 2), (4, 3))
dot list ((3, 2), (3, 4), (5, 2), (5, 4))
dot list ((3, 2), (4, 1), (4, 3), (5, 2))
dot list ((3, 3), (3, 4), (4, 3), (4, 4))
dot list ((3, 3), (3, 5), (5, 3), (5, 5))
dot list ((3, 3), (4, 2), (4, 4), (5, 3))
dot list ((3, 4), (3, 5), (4, 4), (4, 5))
dot list ((3, 4), (4, 3), (4, 5), (5, 4))
dot list ((4, 1), (4, 2), (5, 1), (5, 2))
dot list ((4, 2), (4, 3), (5, 2), (5, 3))
dot list ((4, 3), (4, 4), (5, 3), (5, 4))
dot list ((4, 4), (4, 5), (5, 4), (5, 5))

Answer 2

含有一个小方格的正方形有 16 个
含有四个小方格的正方形有 9 个
含有九个小方格的正方形有 4个
含有16个小方格的正方形有 1 个
共有：20个。本回答被网友采纳

Answer 3

共有：16+9+4+1=30个。

Answer 4

21个

Answer 5

30