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No direct evaluation (Posted on 2015-06-09) Difficulty: 2 of 5
Given that 2^29 is a nine-digit 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

No Solution Yet Submitted by Ady TZIDON    
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Solution Solution | Comment 1 of 4
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 2015-06-09 08:15:51
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