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
The missing digit can be found using the digital root.
2^0=1
2^1=2
2^2=4
2^3=8
2^4=7 (mod 9)
2^5=5 (mod 9)
2^6=1 (mod 9)
so it repeats every 6.
2^29 = 2^5 = 5 (mod 9)
so the missing digit is 4.

Posted by Jer
on 20150609 08:15:51 