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2个回答
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这个问题其实很简单,你可以用这个问题列两个方程式如:4X+3Y+1/3Z=100,X+Y+Z=100,采用消元逐解法就把问题变得很简单了,其中Z必须为3的整倍数,其中一个答案X=8,Y=14,Z=78,即男人8个,女人14个,孩子78个。
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解析:
假设在这一百个人当中,小孩的个数是3的倍数,比如,3,6,9……如果不是3的倍数的话,那么也就没办法搬砖头了,那么这题就没什么意义了
设男的有a人,女的b人,小孩c人
所以,a+b+c=100
4a+3b+c/3=100
由于人数应该都是整数,那么当小孩人数为3,6,9……时(之所以选择小孩的人数做变量,因为小孩的变化值大,而且快)
男人,女人,小孩的人数为:
21-5-3
18-9-3
15-13-3
12-17-3
9-21-3
6-25-3
20-6-6
17-10-6
14-14-6
11-18-6
8-22-6
5-26-6
22-3-9
19-7-9
16-11-9
13-15-9
10-19-9
7-23-9
4-27-9
21-4-12
18-8-12
15-12-12
12-16-12
9-20-12
6-24-12
20-5-15
17-9-15
14-13-15
11-17-15
8-21-15
5-25-15
19-6-18
16-10-18
13-14-18
10-18-18
7-22-18
4-26-18
21-3-21
18-7-21
15-11-21
12-15-21
9-19-21
6-23-21
20-4-24
17-8-24
14-12-24
11-16-24
8-20-24
5-24-24
19-5-27
16-9-27
13-13-27
10-17-27
7-21-27
4-25-27
18-6-30
15-10-30
12-14-30
9-18-30
6-22-30
20-3-33
17-7-33
14-11-33
11-15-33
8-19-33
5-23-33
19-4-36
16-8-36
13-12-36
10-16-36
7-20-36
4-24-36
18-5-39
15-9-39
12-13-39
9-17-39
6-21-39
17-6-42
14-10-42
11-14-42
8-18-42
5-22-42
19-3-45
16-7-45
13-11-45
10-15-45
7-19-45
4-23-45
18-4-48
15-8-48
12-12-48
9-16-48
6-20-48
17-5-51
14-9-51
11-13-51
8-17-51
5-21-51
16-6-54
13-10-54
10-14-54
7-18-54
4-22-54
18-3-57
15-7-57
12-11-57
9-15-57
6-19-57
17-4-60
14-8-60
11-12-60
8-16-60
5-20-60
16-5-63
13-9-63
10-13-63
7-17-63
4-21-63
15-6-66
12-10-66
9-14-66
6-18-66
17-3-69
14-7-69
11-11-69
8-15-69
5-19-69
16-4-72
13-8-72
10-12-72
7-16-72
4-20-72
15-5-75
12-9-75
9-13-75
6-17-75
14-6-78
11-10-78
8-14-78
5-18-78
16-3-81
13-7-81
10-11-81
7-15-81
4-19-81
15-4-84
12-8-84
9-12-84
6-16-84
14-5-87
11-9-87
8-13-87
5-17-87
13-6-90
10-10-90
7-14-90
4-18-90
15-3-93
12-7-93
9-11-93
6-15-93
14-4-96
11-8-96
8-12-96
5-16-96
13-5-99
10-9-99
7-13-99
4-17-99
--------以下是Excel中计算的方法-----------------------
Private Sub CommandButton1_Click()
Dim a, b, c
For c = 3 To 99 Step 3
For b = 3 To 33 Step 1
For a = 4 To 25 Step 1
If c / 3 + b * 3 + a * 4 = 100 Then
TextBox1.Text = TextBox1.Text & a & "-" & b & "-" & c & vbLf
End If
Next a
Next b
Next c
End Sub
假设在这一百个人当中,小孩的个数是3的倍数,比如,3,6,9……如果不是3的倍数的话,那么也就没办法搬砖头了,那么这题就没什么意义了
设男的有a人,女的b人,小孩c人
所以,a+b+c=100
4a+3b+c/3=100
由于人数应该都是整数,那么当小孩人数为3,6,9……时(之所以选择小孩的人数做变量,因为小孩的变化值大,而且快)
男人,女人,小孩的人数为:
21-5-3
18-9-3
15-13-3
12-17-3
9-21-3
6-25-3
20-6-6
17-10-6
14-14-6
11-18-6
8-22-6
5-26-6
22-3-9
19-7-9
16-11-9
13-15-9
10-19-9
7-23-9
4-27-9
21-4-12
18-8-12
15-12-12
12-16-12
9-20-12
6-24-12
20-5-15
17-9-15
14-13-15
11-17-15
8-21-15
5-25-15
19-6-18
16-10-18
13-14-18
10-18-18
7-22-18
4-26-18
21-3-21
18-7-21
15-11-21
12-15-21
9-19-21
6-23-21
20-4-24
17-8-24
14-12-24
11-16-24
8-20-24
5-24-24
19-5-27
16-9-27
13-13-27
10-17-27
7-21-27
4-25-27
18-6-30
15-10-30
12-14-30
9-18-30
6-22-30
20-3-33
17-7-33
14-11-33
11-15-33
8-19-33
5-23-33
19-4-36
16-8-36
13-12-36
10-16-36
7-20-36
4-24-36
18-5-39
15-9-39
12-13-39
9-17-39
6-21-39
17-6-42
14-10-42
11-14-42
8-18-42
5-22-42
19-3-45
16-7-45
13-11-45
10-15-45
7-19-45
4-23-45
18-4-48
15-8-48
12-12-48
9-16-48
6-20-48
17-5-51
14-9-51
11-13-51
8-17-51
5-21-51
16-6-54
13-10-54
10-14-54
7-18-54
4-22-54
18-3-57
15-7-57
12-11-57
9-15-57
6-19-57
17-4-60
14-8-60
11-12-60
8-16-60
5-20-60
16-5-63
13-9-63
10-13-63
7-17-63
4-21-63
15-6-66
12-10-66
9-14-66
6-18-66
17-3-69
14-7-69
11-11-69
8-15-69
5-19-69
16-4-72
13-8-72
10-12-72
7-16-72
4-20-72
15-5-75
12-9-75
9-13-75
6-17-75
14-6-78
11-10-78
8-14-78
5-18-78
16-3-81
13-7-81
10-11-81
7-15-81
4-19-81
15-4-84
12-8-84
9-12-84
6-16-84
14-5-87
11-9-87
8-13-87
5-17-87
13-6-90
10-10-90
7-14-90
4-18-90
15-3-93
12-7-93
9-11-93
6-15-93
14-4-96
11-8-96
8-12-96
5-16-96
13-5-99
10-9-99
7-13-99
4-17-99
--------以下是Excel中计算的方法-----------------------
Private Sub CommandButton1_Click()
Dim a, b, c
For c = 3 To 99 Step 3
For b = 3 To 33 Step 1
For a = 4 To 25 Step 1
If c / 3 + b * 3 + a * 4 = 100 Then
TextBox1.Text = TextBox1.Text & a & "-" & b & "-" & c & vbLf
End If
Next a
Next b
Next c
End Sub
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