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1、一个非负整数的有序对(m,n)称为“简单的”,如果在做m+n的加法时用不着进位。m+n称为有序对(m,n)的和,求和为1942的“简单的”非负整数有序对的个数。解:m+n=1942,对于m的个位可取0,1,2,而”则可取2,1,0三种;对于m的十位可取0,1,2,3 4,而n则可取4、3、2、1、0五种;对于m的百位可取0,1,2,…,9,而n则可取9、8,…,1,0+种;对于m的千位可取1或0,而n则可取0或1。因此简单的非负整数序对(m,n)的个数是 C_3~1C_5~1C_(10)~1C_2~1=3×5×10×2=300。 2、一点在半径为19,中心为(-2,-10,5)的球面上,另一点在半径为87,中心为(12,8,-16)
1. An ordered pair (m,n) of non-negative integers is called “simple” if it does not require a carry when m+n is added. m+n is called the sum of ordered pairs (m,n), and the sum is the number of “simple” non-negative integer ordered pairs of 1942. Solution: m+n=1942. For units of m, we can take 0,1,2, and ”were better than 2,1,0; for ten, we can take 0,1,2,3 4, and n It is preferable to use 4, 3, 2, 1, 0 for five; for the hundred-digit of m, it may take 0, 1, 2, ..., 9, and n may take 9, 8, ..., 1, 0 +; for thousands of m It may be 1 or 0, and n may be 0 or 1. Therefore, the number of simple non-negative integer pairs (m, n) is C_3~1C_5~1C_(10)~1C_2~1=3*5*10*2. ========================================================================================================================================================================================================================================================