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Number Count Conclusion (Posted on 2015-04-15) Difficulty: 3 of 5
sod(N) denotes the sum of the base ten digits of N.

N is a 5-digit base ten positive integer divisible by 15, and sod(N) =15

Determine the total count of the values of N for which this is possible.

No Solution Yet Submitted by K Sengupta    
Rating: 3.0000 (1 votes)

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Solution computer solution | Comment 1 of 4
DefDbl A-Z
Dim crlf$
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

Private Sub Form_Load()
 Text1.Text = ""
 crlf$ = Chr(13) + Chr(10)
 Form1.Visible = True
 
 For n = 10000 To 99999 Step 5
   If sod(n) = 15 Then
     Text1.Text = Text1.Text & n & crlf
     DoEvents
     ct = ct + 1
   End If
 Next n
 
 Text1.Text = Text1.Text & ct & " done" & crlf
 
End Sub

Function sod(x)
  tot = 0
  s$ = LTrim(Str(x))
  For i = 1 To Len(s)
    d = Val(Mid(s, i, 1))
    tot = tot + d
  Next
  sod = tot
End Function

finds 738 such integers

10095
10185
10275
10365
10455
10545
10590
10635
10680
10725
10770
10815
10860
10905
10950
11085
11175
11265
11355
11445
11490
11535
11580
11625
11670
11715
11760
11805
11850
11940
12075
12165
12255
12345
12390
12435
12480
12525
12570
12615
12660
12705
12750
12840
12930
13065
13155
13245
13290
13335
13380
13425
13470
13515
13560
13605
13650
13740
13830
13920
14055
14145
14190
14235
14280
14325
14370
14415
14460
14505
14550
14640
14730
14820
14910
15045
15090
15135
15180
15225
15270
15315
15360
15405
15450
15540
15630
15720
15810
15900
16035
16080
16125
16170
16215
16260
16305
16350
16440
16530
16620
16710
16800
17025
17070
17115
17160
17205
17250
17340
17430
17520
17610
17700
18015
18060
18105
18150
18240
18330
18420
18510
18600
19005
19050
19140
19230
19320
19410
19500
20085
20175
20265
20355
20445
20490
20535
20580
20625
20670
20715
20760
20805
20850
20940
21075
21165
21255
21345
21390
21435
21480
21525
21570
21615
21660
21705
21750
21840
21930
22065
22155
22245
22290
22335
22380
22425
22470
22515
22560
22605
22650
22740
22830
22920
23055
23145
23190
23235
23280
23325
23370
23415
23460
23505
23550
23640
23730
23820
23910
24045
24090
24135
24180
24225
24270
24315
24360
24405
24450
24540
24630
24720
24810
24900
25035
25080
25125
25170
25215
25260
25305
25350
25440
25530
25620
25710
25800
26025
26070
26115
26160
26205
26250
26340
26430
26520
26610
26700
27015
27060
27105
27150
27240
27330
27420
27510
27600
28005
28050
28140
28230
28320
28410
28500
29040
29130
29220
29310
29400
30075
30165
30255
30345
30390
30435
30480
30525
30570
30615
30660
30705
30750
30840
30930
31065
31155
31245
31290
31335
31380
31425
31470
31515
31560
31605
31650
31740
31830
31920
32055
32145
32190
32235
32280
32325
32370
32415
32460
32505
32550
32640
32730
32820
32910
33045
33090
33135
33180
33225
33270
33315
33360
33405
33450
33540
33630
33720
33810
33900
34035
34080
34125
34170
34215
34260
34305
34350
34440
34530
34620
34710
34800
35025
35070
35115
35160
35205
35250
35340
35430
35520
35610
35700
36015
36060
36105
36150
36240
36330
36420
36510
36600
37005
37050
37140
37230
37320
37410
37500
38040
38130
38220
38310
38400
39030
39120
39210
39300
40065
40155
40245
40290
40335
40380
40425
40470
40515
40560
40605
40650
40740
40830
40920
41055
41145
41190
41235
41280
41325
41370
41415
41460
41505
41550
41640
41730
41820
41910
42045
42090
42135
42180
42225
42270
42315
42360
42405
42450
42540
42630
42720
42810
42900
43035
43080
43125
43170
43215
43260
43305
43350
43440
43530
43620
43710
43800
44025
44070
44115
44160
44205
44250
44340
44430
44520
44610
44700
45015
45060
45105
45150
45240
45330
45420
45510
45600
46005
46050
46140
46230
46320
46410
46500
47040
47130
47220
47310
47400
48030
48120
48210
48300
49020
49110
49200
50055
50145
50190
50235
50280
50325
50370
50415
50460
50505
50550
50640
50730
50820
50910
51045
51090
51135
51180
51225
51270
51315
51360
51405
51450
51540
51630
51720
51810
51900
52035
52080
52125
52170
52215
52260
52305
52350
52440
52530
52620
52710
52800
53025
53070
53115
53160
53205
53250
53340
53430
53520
53610
53700
54015
54060
54105
54150
54240
54330
54420
54510
54600
55005
55050
55140
55230
55320
55410
55500
56040
56130
56220
56310
56400
57030
57120
57210
57300
58020
58110
58200
59010
59100
60045
60090
60135
60180
60225
60270
60315
60360
60405
60450
60540
60630
60720
60810
60900
61035
61080
61125
61170
61215
61260
61305
61350
61440
61530
61620
61710
61800
62025
62070
62115
62160
62205
62250
62340
62430
62520
62610
62700
63015
63060
63105
63150
63240
63330
63420
63510
63600
64005
64050
64140
64230
64320
64410
64500
65040
65130
65220
65310
65400
66030
66120
66210
66300
67020
67110
67200
68010
68100
69000
70035
70080
70125
70170
70215
70260
70305
70350
70440
70530
70620
70710
70800
71025
71070
71115
71160
71205
71250
71340
71430
71520
71610
71700
72015
72060
72105
72150
72240
72330
72420
72510
72600
73005
73050
73140
73230
73320
73410
73500
74040
74130
74220
74310
74400
75030
75120
75210
75300
76020
76110
76200
77010
77100
78000
80025
80070
80115
80160
80205
80250
80340
80430
80520
80610
80700
81015
81060
81105
81150
81240
81330
81420
81510
81600
82005
82050
82140
82230
82320
82410
82500
83040
83130
83220
83310
83400
84030
84120
84210
84300
85020
85110
85200
86010
86100
87000
90015
90060
90105
90150
90240
90330
90420
90510
90600
91005
91050
91140
91230
91320
91410
91500
92040
92130
92220
92310
92400
93030
93120
93210
93300
94020
94110
94200
95010
95100
96000
738 done


  Posted by Charlie on 2015-04-15 16:25:15
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