“分块计算法”:对有规律的图形进行计数时,有些题可以采用“分块计数”的方法.
尝试:图1有6个点,图2有12个点,图3有18个点,……,按此规律,求图10,、图
有多少个点?
![](http://tikupic.21cnjy.com/ct20241o/f9/ee/f9eebdf1263b3eea05295800b6e81a60.png)
(1)我们将每个图形分成完全相同的6块,每块黑点的个数相同(如图一、二、三),这样图1中黑点个数是
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmtext%3E6%C3%971%3D6%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
个;图2中黑点个数是
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmtext%3E6%C3%972%3D12%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
个;图3中黑点个数是
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmtext%3E6%C3%973%3D18%3C%2Fmtext%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
个;……;容易求出图10、图
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
中黑点的个数分别是___________、___________.
应用:请你参考以上“分块计数法”,先将下面的点阵进行分块,再完成(2)(3)问题:
(2)第5个点阵中有___________个小圆圈;第
![](http://math.21cnjy.com/mml2svg?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmi%3En%3C%2Fmi%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
个点阵中有___________个小圆圈;
(3)小圆圈的个数能不能等于331吗?如果能,请求出是第几个点阵;如果不能,请说明理由.
![](http://tikupic.21cnjy.com/ct20241o/dd/1a/dd1a579707b0d47f37d64493a781a137.png)