A 10-digit number 2404563210 has an interesting feature: reading from left to right - any k-digit string is divisible by k.
No big deal ! IMHO there are 2492 numbers like that.
At least one of them utilizes only 3 distinct digits.
Find this number.
Some internet research shows that in addition to the 2492 numbers that exhibit the feature (without the restriction of number of distinct digits used), there's a number that extends the divisibility criterion all the way to 25 digits: it is 3,608,528,850,368,400,786,036,725.
The limits of VB prevent me from going beyond 15 digit numbers but the number of qualifying numbers with a given number of digits goes as follows for 10- to 15-digit numbers:
digits number of qualifying numbers
10 2492
11 2225
12 2041
13 1575
14 1132
15 770
The 770 15-digit numbers are listed below, with the number of unique digits used. There are two that use just 4 unique digits each, 384000408000300 and 600804486048060:
102006162060465 6
102456963072105 9
102852405048960 8
102858723000885 7
105258321084840 7
105600645048645 6
108000963072660 8
108006561084525 7
108054801036000 7
108402723000045 8
108852804060000 7
120054249048585 7
120456081024585 7
120456729036840 10
120858561012840 7
123204249084840 7
123204969036525 8
123252561084945 9
123258168000525 7
123600402096645 8
123606009012225 7
123606081060840 7
126000720012720 5
126000729036000 7
126402561012000 6
126408168048540 7
126450882036780 9
126456480048645 7
126858960036900 8
129252240048120 7
129252969012720 7
129600162012165 6
129606480084900 7
129654000084705 9
141204006024900 6
141204726084525 8
141654168048960 7
144006804048945 7
144408645048225 7
144456246000360 7
144804807072945 8
144804888036900 7
144852408036705 9
144852480084060 7
144858087000900 7
147204486000045 8
147252726060720 7
147654567060000 6
162054963072660 9
162402165096645 7
162402804084360 7
162408402096225 8
162450405048120 7
162450486000465 7
162456723000045 8
162804645084900 8
165258882036360 7
165600486048480 6
165606723048060 9
168000084012885 7
168006321012465 8
168408801000720 7
168450165072840 8
168450885024525 7
168456402072420 8
168858963024780 10
180006489084525 8
180054720012720 7
180054729036000 10
180456561012000 7
180852723048480 8
183204009012780 8
183204081060000 7
183252321012885 6
183600243096480 8
183600963048165 8
183654162012165 8
186054489060720 9
186450642072525 8
186804882000105 7
186858720072780 7
186858729096060 8
189204408036840 8
189252720036945 10
189258327060465 10
189606240012840 7
189606249036120 8
189606960072465 9
189654561036225 9
201204567084360 9
201252168048120 7
201258486000045 7
201600000036540 7
201600720096165 7
204006645048780 7
204054966060405 6
204402807072105 7
204408486048060 5
204804648072780 6
204852249036540 8
204852960072885 8
204852969096165 8
207258165072420 8
207258885024105 7
207600480012945 9
207600489036225 9
207606006084120 7
222000885048885 5
222006402096780 7
222054084012885 6
222408243096060 7
222804405012840 6
222852006084540 6
222852726036225 7
225258642072105 8
225600246084225 6
228000564000300 7
228054483036945 8
228402324048645 7
228804804036900 7
228852486060945 7
228858003000900 6
228858723060525 7
240000642096885 7
240006249012465 7
240402483096165 9
240408000036120 7
240408729000720 6
240450723048900 8
240804963084420 7
240858882000105 6
243252801000300 7
243258408036840 7
246006648036525 7
246054240084945 7
246402882000660 5
246408480012525 7
246450402000465 5
246450483072360 8
246456081084225 7
249204240012000 5
249252561036780 10
249600402048480 6
249606729024945 7
261252648036945 9
261606168012840 6
261606888072465 8
261654480012945 8
261654489036225 9
264000168084945 8
264000807072660 6
264006405084525 6
264408966036885 8
264450240012420 6
264450960072045 7
267204087048645 7
267204726036360 6
267606567036900 7
282054564000300 7
282402405012000 6
282408723084885 7
282450726036780 8
282456324048645 7
282852567036060 7
282858804036900 8
285252165000465 7
285258402000045 5
285600006012165 6
285600087084060 7
285606324084900 8
288402165048480 7
288408402048060 5
288450486060105 7
288858564060360 7
300408561096840 8
300456882000660 7
300804084024645 7
300804723012360 8
300852324084060 7
303258240012000 7
303654402048480 7
306000801048885 7
306006489036360 6
306054000012885 8
306054009036165 7
306054081084780 8
306402642048165 8
306408249072945 9
306804483048705 7
306852084000840 7
306858321000420 8
309204009072420 6
309204720000825 8
309204729024105 8
309252321072525 7
309606561000105 6
309654882024885 8
321204168012000 7
321252480012105 7
321252489036780 10
321258087048645 9
321258726036360 8
324006246084360 6
324006966036045 7
324408087084900 7
324450009072840 8
324450729024525 7
324804240096705 9
324804249000420 6
324804969060045 8
324852561000525 8
324858807024780 7
327252807096885 8
327606327072780 6
327654648096165 10
342000486084465 7
342006003024420 5
342006723084045 8
342402966072720 7
342456165048480 8
342804726000105 9
345258963060765 9
345600567072885 8
345606804072465 8
345606885036420 7
345654405036225 6
348000165048900 8
348006483000825 7
348054084072525 7
348054723060240 8
348804486036585 6
360000243024525 6
360006561096000 6
360054801048885 7
360408321024780 8
360456642048165 8
360852804072885 8
360852885036840 7
360858483048705 7
363204162096165 8
363252402048900 8
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363258720000825 7
363258729024105 10
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363606642084420 6
366006249072105 9
366408009000885 7
366408720048840 7
366450084000000 6
366804243084585 7
369204561000660 8
369252162072360 8
369252882024045 8
369600003084060 6
381204648000825 8
381252249072525 9
381600162024900 8
381600882084525 8
381606489000105 8
384000408000300 4
384054327036945 9
384402960048945 8
384408567072465 8
384456168036225 8
384804000024645 7
384804081096540 8
402054165048900 8
402402087012945 8
402402726000660 5
402408324012525 7
402450327072360 7
402852168072900 9
402858486036585 7
405252405036780 8
405258003048645 7
405654246036060 6
405654966096945 5
408000645036465 6
408408003084900 5
408450726096420 8
408804966024000 6
420000084024360 6
420408882084105 6
420450804072045 6
420450885036000 7
420858243084585 6
423258561000660 8
423600165012780 9
423606402012360 6
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426000402084465 6
426000483048420 6
426006009000045 6
426006720048000 6
426456882060300 7
426804723072000 7
429204321048165 9
429258960024720 8
429258969048000 7
429600564036840 8
429606162048705 9
429606801036420 8
429654483060465 8
441204480096945 8
441204489000660 7
441252009000465 7
441252720048420 7
441600642012465 6
444000240096420 5
444000960048105 7
444054168036780 8
444402009048480 5
444450321048585 7
444852801036840 8
444858408060360 6
447204807060765 7
447204888024720 5
447252408024525 6
447252489096420 8
447258726096000 8
447600321084840 8
447606648060045 6
447654240000525 6
462000087012105 8
462054645036465 6
462408165012360 8
462804327048705 8
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465204645072720 6
465252966096105 7
465600168000525 7
465606405000105 5
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564456969012300 8
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582006645000345 7
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585258804024720 6
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987606243036420 8
987606963096045 8
10 2492
11 2225
12 2041
13 1575
14 1132
15 770
DefDbl A-Z
Dim crlf$, n, ct(10 To 16), pass
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr(13) + Chr(10)
For pass = 1 To 2
n = 0
addOn 1
Next
For i = 10 To 15
Text1.Text = Text1.Text & i & Str(ct(i)) & crlf
Next
Text1.Text = Text1.Text & crlf & " done"
End Sub
Sub addOn(wh)
DoEvents
saveN = n
If wh = 1 Then st = 1 Else st = 0
For newd = st To 9
n = 10 * saveN + newd
q = Int(n / wh): r = n - q * wh
If r = 0 Then
If wh >= 10 Then
uCt = 0: ReDim used(9)
s$ = LTrim(Str(n))
For i = 1 To Len(s)
If used(Val(Mid(s, i, 1))) = 0 Then uCt = uCt + 1
used(Val(Mid(s, i, 1))) = 1
Next
If pass = 2 And wh = 15 Then
Text1.Text = Text1.Text & n & Str(uCt) & crlf
Else
If pass = 1 Then ct(wh) = ct(wh) + 1
End If
End If
If wh < 15 Then
addOn wh + 1
End If
End If
Next
n = saveN
End Sub
|
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Posted by Charlie
on 2018-05-18 10:18:57 |
interesting aside
