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 Momentous Multiple (Posted on 2011-11-10)
Determine the minimum possible multiple of the base ten number 2011 that begins with a nonzero digit and contains all the digits from 0 to 9 at least once. What is the next smallest number with this property?

 No Solution Yet Submitted by K Sengupta No Rating

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 computer solution Comment 2 of 2 |

DEFDBL A-Z
CLS
OPEN "momentml.txt" FOR OUTPUT AS #2
strt = -INT(-1000000000# / 2011)
fin = INT(9999999999# / 2011)
FOR j = strt TO fin
n = j * 2011
ns\$ = LTRIM\$(STR\$(n))
good = 1
FOR i = 1 TO 9
IF INSTR(MID\$(ns\$, i + 1), MID\$(ns\$, i, 1)) THEN good = 0: EXIT FOR
NEXT
IF good THEN PRINT j, n: PRINT #2, j, n: ct = ct + 1
NEXT
PRINT ct

Finds there are 1610 pandigital multiples of 2011, starting with

510678       1026973458
514989       1035642879
515439       1036547829
516978       1039642758
518796       1043298756
520623       1046972853
520785       1047298635
521397       1048529367
525726       1057234986
526968       1059732648
529218       1064257398
531225       1068293475
533349       1072564839
533862       1073596482
534042       1073958462
538686       1083297546
538884       1083695724
539163       1084256793
540225       1086392475

...

and ending with

...

4848984       9751306824
4849533       9752410863
4850388       9754130268
4851468       9756302148
4852512       9758401632
4856193       9765804123
4856211       9765840321
4863960       9781423560
4865373       9784265103
4874796       9803214756
4876785       9807214635
4878342       9810345762
4878387       9810436257
4886676       9827105436
4886874       9827503614
4888377       9830526147
4890951       9835702461
4893597       9841023567
4893885       9841602735
4893912       9841657032
4895883       9845620713
4898124       9850127364
4898421       9850724631
4899240       9852371640
4899861       9853620471
4900383       9854670213
4901130       9856172430
4901742       9857403162
4908312       9870615432
4909230       9872461530
4911012       9876045132

listed only for 10-digit numbers, as a higher number of digits means larger numbers, only to repeat unnecessarily some of the digits.

 Posted by Charlie on 2011-11-10 15:37:29

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