Math Trivia : Cut one paper into three pieces

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Cut one paper into three pieces


 There is a rectangular paper on which square grids are drawn. 
This paper is cut twice straight along the grid. 
When it's a paper in the figure below, you can make 3 kinds of figure. 

(1) When cutting the rectangular paper below twice, how many kinds of figure can you make? 

(2) When it's cut once again, how many kinds of figure can you make?



(1) Seven kinds
When you cut twice, ten squares are divided into three parts. 

10=8+1+1=7+2+1=6+3+1=6+2+2=5+4+1=5+3+2=4+4+2=4+3+3 
Among these groups, groups of 7+2+1 and 6+3+1 are not appropriate because it is not cut straight. 

As for the group of 4+4+1, two types of figures can be made. 

Thus, it is seven kinds in total. 

(2) 10 kinds
When you cut three times, ten squares are divided into four parts. 10=7+1+1+1=6+2+1+1=5+3+1+1=5+2+2+1=4+4+1+1=4+3+2+1=4+2+2+2=3+3+3+1=3+3+2+2 

Among these groups, groups of 7+1+1+1 and 3+3+3+1 are not appropriate because it is not cut straight. 

As for the groups of 4+4+1+1, 4+3+2+1 and 4+2+2+2, two types of figures can be made. 

 Thus, it is 10 kinds in total.