In an "old school" projection booth two goats were munching a celluloid version of "Gone with the wind".
After a while both agreed that the book was definitely better.
Assuming that the quality ratio is 9
(according to my taste) list all possible solutions (19, I believe) of the following alphametic:
STORY/FILM=9 ....... (i)
Rem: 3 solutions out of 19 are zero-free !
d4 Bonus:
Instead of the number 9 select another integer N and define #(N) as the number of distinct solutions of the alphametic (i) with a ratio n.
Solve the alphametic.
List the values of #(N) for N=2,3,4,....8.
The 19 solutions for n = 9 are:
27549/3061
27954/3106
36729/4081
36972/4108
47601/5289
54279/6031
54729/6081
54927/6103
54972/6108
57429/6381 *
58239/6471 *
72369/8041
72549/8061
72936/8104
72954/8106
75069/8341
75249/8361 *
82503/9167
85203/9467
I've marked the three with no 0's with an asterisk to make them easier to find.
Going beyond the requested values of #(N) up to N=8, the counts for all possible integral N are
N #(N)
2 32
3 18
4 34
5 51
6 11
7 30
8 76
9 19
12 12
13 24
14 30
15 40
16 17
17 45
18 20
19 15
20 24
22 14
23 16
24 16
25 11
26 15
27 12
28 7
29 13
30 14
32 6
33 4
34 12
35 8
36 2
37 5
38 5
39 4
40 7
42 5
43 4
44 12
45 5
46 2
47 6
48 4
49 3
50 5
52 8
53 7
54 3
55 5
56 3
57 5
58 1
59 2
62 7
63 1
64 1
65 3
66 3
67 2
68 2
69 2
70 2
72 4
76 1
78 1
79 1
82 1
85 1
92 2
93 1
94 1
The lowest N with only 1 solution is 58:
92046/1587 = 58
N = 8 has the most solutions, 76:
16584/2073
18456/2307
18760/2345
24568/3071
24856/3107
25408/3176
25496/3187
27608/3451
32568/4071
32856/4107
36712/4589
36728/4591
37208/4651
37512/4689
37528/4691
38016/4752
38120/4765
38152/4769
41896/5237
42968/5371
46312/5789
46328/5791
46712/5839
47136/5892
47328/5916
47368/5921
50184/6273
50728/6341
51024/6378
51072/6384
51832/6479
53928/6741
54312/6789
54328/6791
54712/6839
56184/7023
56248/7031
56328/7041
56824/7103
56832/7104
56984/7123
58104/7263
58416/7302
58496/7312
58912/7364
59328/7416
59368/7421
60184/7523
60248/7531
60328/7541
62504/7813
63152/7894
63528/7941
65072/8134
65392/8174
65432/8179
65704/8213
67152/8394
67320/8415
67352/8419
67512/8439
71456/8932
71536/8942
71624/8953
71632/8954
73248/9156
73264/9158
73456/9182
74528/9316
74568/9321
74816/9352
75328/9416
75368/9421
76184/9523
76248/9531
76328/9541
DefDbl A-Z
Dim crlf$, solCt(1000)
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
st$ = "1234567890": h$ = st
Do
s = Val(Mid(st, 1, 1))
t = Val(Mid(st, 2, 1))
o = Val(Mid(st, 3, 1))
r = Val(Mid(st, 4, 1))
y = Val(Mid(st, 5, 1))
f = Val(Mid(st, 6, 1))
i = Val(Mid(st, 7, 1))
l = Val(Mid(st, 8, 1))
m = Val(Mid(st, 9, 1))
If s > 0 And f > 0 Then
story = 10000 * s + 1000 * t + 100 * o + 10 * r + y
film = 1000 * f + 100 * i + 10 * l + m
q = story / film
If q = Int(q) Then
solCt(q) = solCt(q) + 1
If q = 9 Then Text1.Text = Text1.Text & story & "/" & film & crlf
End If
End If
DoEvents
permute st
Loop Until st = h
For j = 1 To 1000
If solCt(j) > 0 Then Text1.Text = Text1.Text & mform(j, "###0") & mform(solCt(j), "###0") & crlf
Next
Text1.Text = Text1.Text & crlf & " done"
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
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Posted by Charlie
on 2019-02-18 16:43:31 |
computer solutions, with an extension of the bonus
