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Momentous Multiple (Posted on 2011-11-10) Difficulty: 3 of 5
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    
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Solution 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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