All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Non zero product (Posted on 2015-10-07)
Find the total number of 8-digit positive integers (each containing no zeros) such that the product of four leftmost digits is equal to 6 times the product of the four rightmost digits.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 computer assisted calculation Comment 1 of 1
There are 225 possible products of four non-zero digits. They are shown here with the ways the digits can be arranged to produce the given product; for example, the 10 ways of producing 4 are the four positions the 4 can have among three 1's plus the 10 ways of permuting two 2's and two 1's.

1   1
2   4
3   4
4  10
5   4
6  16
7   4
8  20
9  10
10  12
12  36
14  12
15  12
16  31
18  36
20  24
21  12
24  64
25   6
27  16
28  24
30  36
32  40
35  12
36  72
40  40
42  36
45  24
48  88
49   6
50  12
54  52
56  40
60  60
63  24
64  44
70  24
72 112
75  12
80  48
81  19
84  60
90  60
96  96
98  12
100  18
105  24
108  88
112  48
120  84
125   4
126  60
128  40
135  28
140  36
144 132
147  12
150  24
160  48
162  52
168  84
175  12
180  84
189  28
192  88
196  18
200  24
210  48
216 116
224  48
225  18
240  84
243  16
245  12
250   4
252  84
256  31
270  60
280  48
288 120
294  24
300  24
315  36
320  40
324  72
336  84
343   4
350  12
360  96
375   4
378  60
384  64
392  24
400  18
405  24
420  48
432 112
441  18
448  40
450  24
480  60
486  36
490  12
500   4
504  96
512  20
525  12
540  60
560  36
567  24
576  88
588  24
600  24
625   1
630  48
640  24
648  76
672  60
675  12
686   4
700  12
720  72
729  10
735  12
750   4
756  60
768  36
784  18
800  12
810  36
840  48
864  76
875   4
882  24
896  24
900  18
945  24
960  36
972  36
980  12
1000   4
1008  72
1024  10
1029   4
1050  12
1080  52
1120  24
1125   4
1134  36
1152  48
1176  24
1200  12
1215  12
1225   6
1260  36
1280  12
1296  55
1323  12
1344  36
1350  12
1372   4
1400  12
1440  36
1458  16
1470  12
1512  52
1536  16
1568  12
1575  12
1600   6
1620  24
1680  24
1701  12
1715   4
1728  40
1764  18
1792  12
1800  12
1890  24
1920  12
1944  28
1960  12
2016  36
2025   6
2048   4
2058   4
2160  24
2187   4
2205  12
2240  12
2268  24
2304  18
2352  12
2401   1
2430  12
2520  24
2560   4
2592  24
2646  12
2688  12
2744   4
2835  12
2880  12
2916  10
3024  24
3072   4
3087   4
3136   6
3240  12
3402  12
3456  12
3528  12
3584   4
3645   4
3888  12
3969   6
4032  12
4096   1
4374   4
4536  12
4608   4
5103   4
5184   6
5832   4
6561   1

Then, the ways of each is multiplied by the ways of 6 times that value, if that exists:

1*16 + 4*36 +  4*36  + 10*64   + ...

The grand total is 225896.

DefDbl A-Z
Dim crlf\$, nlzero(6561)

Form1.Visible = True

Text1.Text = ""
crlf = Chr\$(13) + Chr\$(10)

For a = 1 To 9
For b = 1 To 9
For c = 1 To 9
For d = 1 To 9
t = a * b * c * d
nlzero(t) = nlzero(t) + 1
If nlzero(t) = 1 Then dct = dct + 1
Next
Next
Next
Next

Text1.Text = dct & crlf

For i = 0 To 6561
If nlzero(i) > 0 Then
Text1.Text = Text1.Text & mform(i, "###0")
Text1.Text = Text1.Text & mform(nlzero(i), "###0") & crlf
End If
Next
Text1.Text = Text1.Text & crlf

For low = 1 To 6561 / 6
totnumber = totnumber + nlzero(low) * nlzero(6 * low)
Next

Text1.Text = Text1.Text & totnumber & 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

 Posted by Charlie on 2015-10-07 20:02:02

 Search: Search body:
Forums (0)