6210001000(1)--> SUM(a_i) = 10(2)--> if a_0 = n, then there must be exactly 9-n non-zero digits in the number which add up to 10-n.Using (1), (2) and the hypothesis of the problem, it is easy to deduce that a_0 can only be 6. The rest of the digits can now be easily found out.

6210001000

ReplyDelete(1)--> SUM(a_i) = 10

(2)--> if a_0 = n, then there must be exactly 9-n non-zero digits in the number which add up to 10-n.

Using (1), (2) and the hypothesis of the problem, it is easy to deduce that a_0 can only be 6. The rest of the digits can now be easily found out.