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 Identical Digit Baffle II (Posted on 2014-10-30)
N is a five-digit positive integer such that when multiplied by a single digit, the result is a six-digit positive integer having precisely 5 identical nonzero digits.

Find the respective minimum and maximum value of N.

 No Solution Yet Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 solution and also those in the middle Comment 2 of 2 |
Just ignore the ones with five zeros:

12346 9 111114
12349 9 111141
12379 9 111411
12500 8 100000
12679 9 114111
13889 8 111112
15679 9 141111
15874 7 111118
15883 7 111181
15973 7 111811
16873 7 118111
18519 6 111114
19753 9 177777
20000 5 100000
22222 5 111110
22223 5 111115
23611 8 188888
24074 6 144444
24692 9 222228
24698 9 222282
24758 9 222822
25000 4 100000
25000 8 200000
25358 9 228222
25873 7 181111
26984 7 188888
27778 4 111112
27778 8 222224
27779 4 111116
27779 8 222232
27784 8 222272
28395 9 255555
31111 5 155555
31358 9 282222
31747 7 222229
31756 7 222292
31846 7 222922
32746 7 229222
36111 4 144444
36111 8 288888
37038 3 111114
37038 6 222228
37039 3 111117
37042 6 222252
37047 3 111141
37047 6 222282
37057 3 111171
37087 6 222522
37137 3 111411
37137 6 222822
37237 3 111711
37500 8 300000
37537 6 225222
38037 3 114111
38037 6 228222
39037 3 117111
40000 5 200000
41667 8 333336
41746 7 292222
42037 6 252222
42857 7 299999
44444 5 222220
44445 5 222225
45679 9 411111
47037 3 141111
47037 6 282222
47222 4 188888
48148 3 144444
48148 6 288888
48611 8 388888
49383 9 444447
49386 9 444474
49416 9 444744
49716 9 447444
50000 2 100000
50000 4 200000
50000 6 300000
50000 8 400000
51111 5 255555
52716 9 474444
55518 8 444144
55543 8 444344
55553 4 222212
55553 8 444424
55555 2 111110
55555 4 222220
55555 6 333330
55555 8 444440
55556 2 111112
55556 4 222224
55556 6 333336
55556 8 444448
55557 2 111114
55557 4 222228
55558 2 111116
55558 4 222232
55558 8 444464
55559 2 111118
55563 4 222252
55568 4 222272
55568 8 444544
55573 4 222292
55593 8 444744
55618 8 444944
57037 3 171111
58395 9 525555
59259 3 177777
60000 5 300000
61111 2 122222
61111 4 244444
61111 6 366666
61111 8 488888
61395 9 552555
61695 9 555255
61725 9 555525
61728 9 555552
62500 8 500000
65432 9 588888
66666 5 333330
66667 5 333335
69074 6 414444
69444 8 555552
71111 5 355555
72222 2 144444
72222 4 288888
73574 6 441444
73611 8 588888
74024 6 444144
74069 6 444414
74075 3 222225
74076 3 222228
74079 6 444474
74084 3 222252
74094 3 222282
74124 6 444744
74174 3 222522
74274 3 222822
74574 6 447444
75000 4 300000
75000 8 600000
75074 3 225222
76074 3 228222
79074 6 474444
79753 9 717777
80000 5 400000
82716 9 744444
83327 8 666616
83332 8 666656
83333 2 166666
83333 4 333332
83333 8 666664
83334 4 333336
83337 8 666696
84074 3 252222
85185 3 255555
85753 9 771777
86111 4 344444
86111 8 688888
86353 9 777177
86413 9 777717
86419 9 777771
87037 6 522222
87500 8 700000
88888 5 444440
88889 5 444445
91111 5 455555
91358 9 822222
92592 6 555552
92593 6 555558
94074 3 282222
94444 2 188888
95432 9 858888
96296 3 288888
97222 4 388888
97222 8 777776
98148 6 588888
98432 9 885888
98611 8 788888
98732 9 888588
98762 9 888858
98765 9 888885

DefDbl A-Z
Dim crlf\$

ChDir "C:\Program Files (x86)\DevStudio\VB\projects\flooble"
Text1.Text = ""
crlf\$ = Chr(13) + Chr(10)
Form1.Visible = True
DoEvents

For n = 10000 To 99999
For m = 1 To 9
prod = n * m
If prod > 99999 And prod < 1000000 Then
s\$ = LTrim(Str(prod))
For i = 1 To Len(s\$)
had(Val(Mid(s\$, i, 1))) = had(Val(Mid(s\$, i, 1))) + 1
Next
For i = 0 To 9
If had(i) = 1 Then had1 = 1
If had(i) = 5 Then had5 = 1
Next
Text1.Text = Text1.Text & n & Str(m) & Str(prod) & crlf
End If
End If
Next
Next

Text1.Text = Text1.Text & crlf & "done"
End Sub

 Posted by Charlie on 2014-10-30 14:35:46

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