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Digits 0-9 (Posted on 2009-11-05) Difficulty: 3 of 5
X is a positive eight-digit base ten integer of the form CONSIDER where each of the capital letters in bold denotes a different base ten digit from 0 to 9, and satisfies all of the following conditions, where C is nonzero.

  • CO is divisible by 2.
  • CON is divisible by 3.
  • CONS is divisible by 4.
  • CONSI is divisible by 5.
  • CONSID is divisible by 6.
  • CONSIDE is divisible by 7.
  • CONSIDER is divisible by 8.
Determine the respective minimum and maximum value of X.

No Solution Yet Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Consideratum Comment 4 of 4 |

There are nine eight-digit numbers which meet the conditions for divisibility, with unique digits.  The first and last would be the minimum and maximum requested.  Execution time 0.01 seconds.

12965408

30925864

36925840

38165472

72965480

78320416

78920456

80165472

92765408


  Posted by ed bottemiller on 2009-11-05 17:46:05
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