I was asked to erase one number from a series 3,13,23,…103 and then to erase two members of the remaining sequence, then three and finally four.
I was requested to make sure that after each step of erasures the sum of the remaining members will be divisible by eleven.

Rather than trying to find the "right" order of erasures prove that it cannot be done.

The sum of the series = 583 = 11*53. 

33 is the only term of the series divisible by 11, so 33 has to be the first member removed.

However, after removing 1+2+3+4 = 10 members, 33 is the only possible choice for last member.

The previous 2 statements are in contradiction, therefore the conditions of the problem cannot be fulfilled. 

 

Posted by xdog on 2011-04-18 12:29:14