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For a string x_1x_2x_3... you should always add if x_i if its 0. However, is this also the case for x_i=1. For instance for 214, 2*1*4> 2+1+4. On the other hand for 21114 2+1+1+1+4 > 2*1*1*1*4. Have I misunderstood the question?
- muchosretardos July 11, 2017