Each member of a group of 37 students was sent to one of three rooms.
Later, each was asked "How many other students were in your room?" The average of these responses was 12.
How is this possible?
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
Text1.Text = ""
crlf$ = Chr(13) + Chr(10)
Form1.Visible = True
For a = 0 To 12
For b = a To (37 - a) / 2
c = 37 - a - b
avge = (a * a + b * b + c * c) / (a + b + c)
DoEvents
Text1.Text = Text1.Text & mform(a, "##0") & mform(b, "##0") & mform(c, "##0") & " " & avge & crlf
'If avge = 13 Then Text1.Text = Text1.Text & a & Str(b) & Str(c) & crlf
Next
Next
Text1.Text = Text1.Text & " done"
DoEvents
End Sub
Function mform$(x, t$)
a$ = Format$(x, t$)
If Len(a$) < Len(t$) Then a$ = Space$(Len(t$) - Len(a$)) & a$
mform$ = a$
End Function
finds all the possible distributions with their respective averages of total numbers of students:
0 0 37 37
0 1 36 35.0540540540541
0 2 35 33.2162162162162
0 3 34 31.4864864864865
0 4 33 29.8648648648649
0 5 32 28.3513513513514
0 6 31 26.9459459459459
0 7 30 25.6486486486486
0 8 29 24.4594594594595
0 9 28 23.3783783783784
0 10 27 22.4054054054054
0 11 26 21.5405405405405
0 12 25 20.7837837837838
0 13 24 20.1351351351351
0 14 23 19.5945945945946
0 15 22 19.1621621621622
0 16 21 18.8378378378378
0 17 20 18.6216216216216
0 18 19 18.5135135135135
1 1 35 33.1621621621622
1 2 34 31.3783783783784
1 3 33 29.7027027027027
1 4 32 28.1351351351351
1 5 31 26.6756756756757
1 6 30 25.3243243243243
1 7 29 24.0810810810811
1 8 28 22.9459459459459
1 9 27 21.9189189189189
1 10 26 21
1 11 25 20.1891891891892
1 12 24 19.4864864864865
1 13 23 18.8918918918919
1 14 22 18.4054054054054
1 15 21 18.027027027027
1 16 20 17.7567567567568
1 17 19 17.5945945945946
1 18 18 17.5405405405405
2 2 33 29.6486486486486
2 3 32 28.027027027027
2 4 31 26.5135135135135
2 5 30 25.1081081081081
2 6 29 23.8108108108108
2 7 28 22.6216216216216
2 8 27 21.5405405405405
2 9 26 20.5675675675676
2 10 25 19.7027027027027
2 11 24 18.9459459459459
2 12 23 18.2972972972973
2 13 22 17.7567567567568
2 14 21 17.3243243243243
2 15 20 17
2 16 19 16.7837837837838
2 17 18 16.6756756756757
3 3 31 26.4594594594595
3 4 30 25
3 5 29 23.6486486486486
3 6 28 22.4054054054054
3 7 27 21.2702702702703
3 8 26 20.2432432432432
3 9 25 19.3243243243243
3 10 24 18.5135135135135
3 11 23 17.8108108108108
3 12 22 17.2162162162162
3 13 21 16.7297297297297
3 14 20 16.3513513513514
3 15 19 16.0810810810811
3 16 18 15.9189189189189
3 17 17 15.8648648648649
4 4 29 23.5945945945946
4 5 28 22.2972972972973
4 6 27 21.1081081081081
4 7 26 20.027027027027
4 8 25 19.0540540540541
4 9 24 18.1891891891892
4 10 23 17.4324324324324
4 11 22 16.7837837837838
4 12 21 16.2432432432432
4 13 20 15.8108108108108
4 14 19 15.4864864864865
4 15 18 15.2702702702703
4 16 17 15.1621621621622
5 5 27 21.0540540540541
5 6 26 19.9189189189189
5 7 25 18.8918918918919
5 8 24 17.972972972973
5 9 23 17.1621621621622
5 10 22 16.4594594594595
5 11 21 15.8648648648649
5 12 20 15.3783783783784
5 13 19 15
5 14 18 14.7297297297297
5 15 17 14.5675675675676
5 16 16 14.5135135135135
6 6 25 18.8378378378378
6 7 24 17.8648648648649
6 8 23 17
6 9 22 16.2432432432432
6 10 21 15.5945945945946
6 11 20 15.0540540540541
6 12 19 14.6216216216216
6 13 18 14.2972972972973
6 14 17 14.0810810810811
6 15 16 13.972972972973
7 7 23 16.9459459459459
7 8 22 16.1351351351351
7 9 21 15.4324324324324
7 10 20 14.8378378378378
7 11 19 14.3513513513514
7 12 18 13.972972972973
7 13 17 13.7027027027027
7 14 16 13.5405405405405
7 15 15 13.4864864864865
8 8 21 15.3783783783784
8 9 20 14.7297297297297
8 10 19 14.1891891891892
8 11 18 13.7567567567568
8 12 17 13.4324324324324
8 13 16 13.2162162162162
8 14 15 13.1081081081081
9 9 19 14.1351351351351
9 10 18 13.6486486486486
9 11 17 13.2702702702703
9 12 16 13
9 13 15 12.8378378378378
9 14 14 12.7837837837838
10 10 17 13.2162162162162
10 11 16 12.8918918918919
10 12 15 12.6756756756757
10 13 14 12.5675675675676
11 11 15 12.6216216216216
11 12 14 12.4594594594595
11 13 13 12.4054054054054
12 12 13 12.3513513513514
13 is the smallest integral average achievable, with 9, 12 and 16 students in each class, the 13 including the student asked, and this distribution being the sought way that this could happen.
Edited on July 21, 2020, 7:34 am
|
|
Posted by Charlie
on 2020-07-01 18:55:33 |
computer solution
