February 2011
You can solve this challenge in several ways. By exhaustive search (checking all the possibilities), you can obtain the smallest answers: 5000261920005 for conditions A,B,and C, and 10962025901110652029601 for conditions A,B,and C'.
A simpler solution is to examine numbers of the form 10^n+1 (100...001), which fulfill conditions A and B, and choose n such that condition C is fulfilled too. The first such solution is 10^335+1.
10^n+1 will never fulfill condition C', so other patterns must be found. A possible solution is 5005*(10^303+1).
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