The first 11-digit duodecimal positive integer is 10000000000 and the last is bbbbbbbbbbb. The former, in decimal is 12^10, and the latter is 12^13 - 1. Those numbers are 61,917,364,224 and 743,008,370,687 respectively.
The first of these numbers is congruent to 2 mod 7, so we can start testing numbers for duodecimal pandigitality at the duodecimal equivalent of 61,917,364,224 + 5 = 61,917,364,229, and continue incrementing by 7. This involves testing almost 100 billion numbers to see if their duodecimal representation is pandigital and reporting any found, using duodecimal representation.
An alternative is to take the string "123456789ab" and form all 479,001,600 permutations to see which ones are divisible by 7. That's only about 1/200 as many numbers to test.
DefDbl A-Z
Dim crlf$
Private Sub Form_Load()
Form1.Visible = True
Text1.Text = ""
crlf = Chr$(13) + Chr$(10)
n$ = "123456789ab": h$ = n
Do
v = fromBase(n, 12)
permute n
DoEvents
q = Int(v / 7)
r = v - 7 * q
If r = 0 Then
Text1.Text = Text1.Text & n & " " & v & " " & v - prev & crlf
prev = v
ct = ct + 1
If ct > 200 Then Exit Sub
End If
Loop Until n = h
Text1.Text = Text1.Text & crlf & " done"
End Sub
Function fromBase(n$, b)
v = 0
For i = 1 To Len(n$)
c$ = LCase$(Mid(n$, i, 1))
If c$ > " " Then
v = v * b + InStr("0123456789abcdefghijklmnopqrstuvwxyz", c$) - 1
End If
Next
fromBase = v
End Function
The above implementation cuts off after 201 values are found. These values are:
decimal
duodecimal decimal difference from
equivalent previous value
12345679ba8 73686782554
1234567a8b9 73686783863 1309
1234567ba98 73686785865 2002
123456879ba 73686799571 13706
12345687b9a 73686799725 154
1234568b97a 73686806193 6468
123456987ab 73686820592 14399
123456987ba 73686821747 1155
12345698ba7 73686822286 539
1234569a87b 73686825212 2926
1234569b78a 73686825751 539
1234569b7a8 73686826906 1155
123456a7b98 73686841305 14399
123456ab897 73686847773 6468
123456b789a 73686847927 154
123456b798a 73686861633 13706
123456b978a 73686863635 2002
123456b987a 73686864944 1309
12345768ba9 73687008934 143990
123457698ba 73687010243 1309
1234576a9b8 73687012091 1848
12345789a6b 73687051438 39347
1234578ab69 73687053594 2156
1234578ab96 73687053825 231
123457968ab 73687055442 1617
12345796ab8 73687067531 12089
1234579a68b 73687071150 3619
1234579b86a 73687075616 4466
123457a698b 73687088013 12397
123457a89b6 73687091555 3542
123457ab698 73687096329 4774
123457b68a9 73687108726 12397
123457b6a89 73687108880 154
123457ba869 73687115348 6468
1234586a7b9 73687260647 145299
1234586ab79 73687260955 308
123458769ab 73687262803 1848
12345876ba9 73687275046 12243
12345879ab6 73687280051 5005
1234587b96a 73687282977 2926
1234587b9a6 73687283362 385
12345896b7a 73687316395 33033
12345897a6b 73687317550 1155
1234589b67a 73687323402 5852
123458a76b9 73687338263 14861
123458a9b67 73687341882 3619
123458b679a 73687345578 3696
123458b6a97 73687357821 12243
123458b7a69 73687359438 1617
123458ba796 73687364289 4851
12345968a7b 73687506046 141757
12345968ab7 73687506431 385
1234596ba78 73687511359 4928
12345976b8a 73687523756 12397
12345978ba6 73687527298 3542
1234597ab68 73687530378 3080
123459876ab 73687544623 14245
12345987ab6 73687546163 1540
1234598a6b7 73687550783 4620
123459ab678 73687589514 38731
123459ab687 73687593980 4466
123459ab867 73687594134 154
123459b786a 73687607840 13706
123459b86a7 73687609534 1694
123459ba768 73687612999 3465
12345a6798b 73687753293 140294
12345a6987b 73687756604 3311
12345a6b789 73687757143 539
12345a6b987 73687760300 3157
12345a76b98 73687772697 12397
12345a7896b 73687775469 2772
12345a7968b 73687776162 693
12345a796b8 73687777163 1001
12345a79b86 73687777856 693
12345a7b869 73687780628 2772
12345a867b9 73687792871 12243
12345a86b79 73687793179 308
12345a8b697 73687801341 8162
12345a9867b 73687815894 14553
12345a986b7 73687816895 1001
12345a9b786 73687822208 5313
12345ab6789 73687822362 154
12345ab8976 73687858783 36421
12345ab9687 73687860092 1309
12345ab9867 73687860246 154
12345b679a8 73688002234 141988
12345b6879a 73688002388 154
12345b6897a 73688003697 1309
12345b78a69 73688024718 21021
12345b798a6 73688026258 1540
12345b7a689 73688026566 308
12345b7a698 73688027721 1155
12345b869a7 73688041966 14245
12345b89a67 73688046894 4928
12345b89a76 73688047279 385
12345b9687a 73688062448 15169
12345b9876a 73688065759 3311
12345b9a678 73688066298 539
12345b9a876 73688069455 3157
12345ba6798 73688083161 13706
12345ba6978 73688083315 154
12345ba7896 73688085009 1694
12345ba8967 73688086626 1617
12345ba9786 73688088320 1694
123465789ab 73688088474 154
12346579b8a 73689519596 1431122
1234657b89a 73689521444 1848
1234657b98a 73689522753 1309
12346587ba9 73689536998 14245
1234658a79b 73689540463 3465
1234658ab97 73689542157 1694
12346597a8b 73689557326 15169
1234659a7b8 73689562331 5005
123465a789b 73689564487 2156
123465a78b9 73689578039 13552
123465a89b7 73689579887 1848
123465a978b 73689580195 308
123465b79a8 73689598906 18711
123465b879a 73689599060 154
123465b897a 73689600369 1309
12346759ba8 73689975898 375529
1234675a8b9 73689977207 1309
1234675ba98 73689979209 2002
123467895ba 73690037267 58058
1234678ab59 73690039577 2310
123467958ab 73690041425 1848
12346795b8a 73690051820 10395
12346798a5b 73690056286 4466
1234679a58b 73690057133 847
1234679b8a5 73690061830 4697
123467a59b8 73690072379 10549
123467a85b9 73690076999 4620
123467a9b85 73690079540 2541
123467b8a95 73690098405 18865
123467ba598 73690101177 2772
123467ba985 73690101716 539
12346857ab9 73690221143 119427
123468597ab 73690221297 154
1234685a97b 73690225917 4620
1234685ba79 73690227919 2002
123468759ba 73690259027 31108
12346875b9a 73690259181 154
1234687b5a9 73690268806 9625
12346895a7b 73690300222 31416
12346895ab7 73690300607 385
123468975ba 73690303379 2772
1234689b57a 73690309385 6006
123468a57b9 73690320935 11550
123468a5b79 73690321243 308
123468a79b5 73690324631 3388
123468a9b57 73690327865 3234
123468ab795 73690331253 3388
123468b579a 73690331561 308
123468b7a59 73690345421 13860
123468b95a7 73690348270 2849
123468b9a75 73690348963 693
123469578ba 73690469699 120736
1234695a78b 73690471855 2156
1234695ba87 73690476860 5005
12346975ba8 73690508122 31262
12346978ab5 73690513127 5005
1234697a5b8 73690515899 2772
1234697ab58 73690516361 462
1234698ab75 73690537459 21098
1234698b75a 73690538383 924
1234698b7a5 73690538614 231
123469a785b 73690572956 34342
123469ab578 73690575497 2541
123469ab857 73690580117 4620
123469b587a 73690590512 10395
123469b78a5 73690594054 3542
123469ba587 73690598828 4774
12346a5879b 73690718948 120120
12346a587b9 73690720103 1155
12346a58b79 73690720411 308
12346a598b7 73690721951 1540
12346a7958b 73690762145 40194
12346a7b598 73690766457 4312
12346a7b985 73690766996 539
12346a859b7 73690777391 10395
12346a8759b 73690777699 308
12346a8795b 73690780317 2618
12346a95b78 73690798027 17710
12346a95b87 73690798412 385
12346a978b5 73690801415 3003
12346a9857b 73690801877 462
12346a98b75 73690803571 1694
12346ab5789 73690808345 4774
12346ab5897 73690839453 31108
12346ab7589 73690839607 154
12346ab8759 73690844227 4620
12346ab9857 73690846229 2002
12346b578a9 73690967350 121121
12346b57a89 73690967504 154
12346b589a7 73690969198 1694
12346b59a78 73690970815 1617
12346b5a897 73690972509 1694
12346b7589a 73690972663 154
12346b78a59 73691010701 38038
12346b7985a 73691011856 1155
12346b7a589 73691012549 693
The differences are irregular, but all positive, as a and b are higher in the collating sequence than normal decimal digits; thus the numbers are found in ascending sequence.
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Posted by Charlie
on 2016-09-13 09:51:04 |
Choice of two algorithms
