perplexus.info :: Numbers : No direct evaluation

No direct evaluation (Posted on 2015-06-09)

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

| 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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