Question

有一串数，1，9，9，8......从第5个数起，每个数都等于它前面四个数之和的个位数字，一直这样写下去。

在前99个数【包括第99个数】中有多少个偶数？？？

Answer 1

伙计，这么多字不容易，记得给分。
前99个数字如下:
{1,9,9,8,7,3,7,5,2,7,1,5,5,8,9,7,9,3,8,7,7,5,7,6,5,3,1,5,4,3,3,5,5,6,9,5,5,5,4,9,3,1,7,0,1,9,7,7,4,7,5,3,9,4,1,7,1,3,2,3,9,7,1,0,7,5,3,5,0,3,1,9,3,6,9,7,5,7,8,7,7,9,1,4,1,5,1,1,8,5,5,9,7,6,7,9,9,1,6}
其中偶数20个,奇数79个.

{序号i,第i个数}
{1,1},
{2,9},
{3,9},
{4,8},
{5,7},
{6,3},
{7,7},
{8,5},
{9,2},
{10,7},
{11,1},
{12,5},
{13,5},
{14,8},
{15,9},
{16,7},
{17,9},
{18,3},
{19,8},
{20,7},
{21,7},
{22,5},
{23,7},
{24,6},
{25,5},
{26,3},
{27,1},
{28,5},
{29,4},
{30,3},
{31,3},
{32,5},
{33,5},
{34,6},
{35,9},
{36,5},
{37,5},
{38,5},
{39,4},
{40,9},
{41,3},
{42,1},
{43,7},
{44,0},
{45,1},
{46,9},
{47,7},
{48,7},
{49,4},
{50,7},
{51,5},
{52,3},
{53,9},
{54,4},
{55,1},
{56,7},
{57,1},
{58,3},
{59,2},
{60,3},
{61,9},
{62,7},
{63,1},
{64,0},
{65,7},
{66,5},
{67,3},
{68,5},
{69,0},
{70,3},
{71,1},
{72,9},
{73,3},
{74,6},
{75,9},
{76,7},
{77,5},
{78,7},
{79,8},
{80,7},
{81,7},
{82,9},
{83,1},
{84,4},
{85,1},
{86,5},
{87,1},
{88,1},
{89,8},
{90,5},
{91,5},
{92,9},
{93,7},
{94,6},
{95,7},
{96,9},
{97,9},
{98,1},
{99,6}

Mathematica 程序如下:
arr = {1, 9, 9, 8};
oush = 1;
jish = 3;
For[i = 5, i < 100, i++,
num = Mod[Sum[arr[[i - j]], {j, 1, 4}], 10];
If[Mod[num, 2] == 0, oush++, jish++];
arr = Append[arr, num];
];
arr
"oush"
oush
"jish"
jish
arr2 = Table[i, {i, 1, 99}];
Transpose[{arr2, arr}]

附
前999个数字如下,其中偶数200个,奇数799个.
{1,9,9,8,7,3,7,5,2,7,1,5,5,8,9,7,9,3,8,7,7,5,7,6,5,3,1,5,4,3,3,5,5,6,9,5,5,5,4,9,3,1,7,0,1,9,7,7,4,7,5,3,9,4,1,7,1,3,2,3,9,7,1,0,7,5,3,5,0,3,1,9,3,6,9,7,5,7,8,7,7,9,1,4,1,5,1,1,8,5,5,9,7,6,7,9,9,1,6,5,1,3,5,4,3,5,7,9,4,5,5,3,7,0,5,5,7,7,4,3,1,5,3,2,1,1,7,1,0,9,7,7,3,6,3,9,1,9,2,1,3,5,1,0,9,5,5,9,8,7,9,3,7,6,5,1,9,1,6,7,3,7,3,0,3,3,9,5,0,7,1,3,1,2,7,3,3,5,8,9,5,7,9,0,1,7,7,5,0,9,1,5,5,0,1,1,7,9,8,5,9,1,3,8,1,3,5,7,6,1,9,3,9,2,3,7,1,3,4,5,3,5,7,0,5,7,9,1,2,9,1,3,5,8,7,3,3,1,4,1,9,5,9,4,7,5,5,1,8,9,3,1,1,4,9,5,9,7,0,1,7,5,3,6,1,5,5,7,8,5,5,5,3,8,1,7,9,5,2,3,9,9,3,4,5,1,3,3,2,9,7,1,9,6,3,9,7,5,4,5,1,5,5,6,7,3,1,7,8,9,5,9,1,4,9,3,7,3,2,5,7,7,1,0,5,3,9,7,4,3,3,7,7,0,7,1,5,3,6,5,9,3,3,0,5,1,9,5,0,5,9,9,3,6,7,5,1,9,2,7,9,7,5,8,9,9,1,7,6,3,7,3,9,2,1,5,7,5,8,5,5,3,1,4,3,1,9,7,0,7,3,7,7,4,1,9,1,5,6,1,3,5,5,4,7,1,7,9,4,1,1,5,1,8,5,9,3,5,2,9,9,5,5,8,7,5,5,5,2,7,9,3,1,0,3,7,1,1,2,1,5,9,7,2,3,1,3,9,6,9,7,1,3,0,1,5,9,5,0,9,3,7,9,8,7,1,5,1,4,1,1,7,3,2,3,5,3,3,4,5,5,7,1,8,1,7,7,3,8,5,3,9,5,2,9,5,1,7,2,5,5,9,1,0,5,5,1,1,2,9,3,5,9,6,3,3,1,3,0,7,1,1,9,8,9,7,3,7,6,3,9,5,3,0,7,5,5,7,4,1,7,9,1,8,5,3,7,3,8,1,9,1,9,0,9,9,7,5,0,1,3,9,3,6,1,9,9,5,4,7,5,1,7,0,3,1,1,5,0,7,3,5,5,0,3,3,1,7,4,5,7,3,9,4,3,9,5,1,8,3,7,9,7,6,9,1,3,9,2,5,9,5,1,0,5,1,7,3,6,7,3,9,5,4,1,9,9,3,2,3,7,5,7,2,1,5,5,3,4,7,9,3,3,2,7,5,7,1,0,3,1,5,9,8,3,5,5,1,4,5,5,5,9,4,3,1,7,5,6,9,7,7,9,2,5,3,9,9,6,7,1,3,7,8,9,7,1,5,2,5,3,5,5,8,1,9,3,1,4,7,5,7,3,2,7,9,1,9,6,5,1,1,3,0,5,9,7,1,2,9,9,1,1,0,1,3,5,9,8,5,7,9,9,0,5,3,7,5,0,5,7,7,9,8,1,5,3,7,6,1,7,1,5,4,7,7,3,1,8,9,1,9,7,6,3,5,1,5,4,5,5,9,3,2,9,3,7,1,0,1,9,1,1,2,3,7,3,5,8,3,9,5,5,2,1,3,1,7,2,3,3,5,3,4,5,7,9,5,6,7,7,5,5,4,1,5,5,5,6,1,7,9,3,0,9,1,3,3,6,3,5,7,1,6,9,3,9,7,8,7,1,3,9,0,3,5,7,5,0,7,9,1,7,4,1,3,5,3,2,3,3,1,9,6,9,5,9,9,2,5,5,1,3,4,3,1,1,9,4,5,9,7,5,6,7,5,3,1,6,5,5,7,3,0,5,5,3,3,6,7,9,5,7,8,9,9,3,9,0,1,3,3,7,4,7,1,9,1,8,9,7,5,9,0,1,5,5,1,2,3,1,7,3,4,5,9,1,9,4,3,7,3,7,0,7,7,1,5,0,3,9,7,9,8,3,7,7,5,2,1,5,3,1,0,9,3,3,5,0,1,9,5,5,0,9,9,3,1,2,5,1,9,7,2,9,7,5,3,4,9,1,7,1,8,7,3,9,7,6}

追问

抱歉这个答案我已经知道啦，下次表抄袭喽

Answer 2

这串数为1,9,9,8,7,3,7,5,2,7,1,5，，5,8,9,7,9,3,8..你会发现每隔4个数就有一个偶数，偶数的位置都在第4或者第9个，则共有（99+1）/5=20个偶数

Answer 3

1,9,9,8,7,3,7,5,2,7,1,5,5,8,9,7,9,3,8,7,7,5,7,6,5,3,1,5,4,3,3,5,5,6,9,5,5,5,4,9,3,1,7,0,1,9,7,7,4,7,5,3,9,4,1,7,1,3,2,3,9,7,1,0,7,5,3,5,0,3,1,9,3,6,9,7,5,7,8,7,7,9,1,4,1,5,1,1,8,5,5,9,7,6,7,9,9,1,6偶数20个,奇数79个.