Given that
2^29 is a ninedigit number all of whose digits are distinct,
determine which of the ten digits is
missing.
Provide your answer without computing the actual number.
Source: SMO contest
(In reply to
Solution by Jer)
your answer is right but I must disagree with your reasoning as stated. It needs to be clarified that this approach only works if the number has a nonzero digital root.
For example, take the 9digit number 102345678. It has 9 distinct digits which sum to 36 which is a multiple of 9 thus
102345678 = 0 mod 9
however the missing digit is not zero
so in general
if N is a 9digit number consisting of 9 distinct digits, then
N= r mod 9
means that r is the missing digit UNLESS r=0 in which case the missing digit could be either 0 or 9

Posted by Daniel
on 20150609 09:43:07 