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Extraterrestrial primes (Posted on 2004-01-19) Difficulty: 3 of 5
An earthling with a superpower telescope observed a chalkboard on a distant planet. On it were some mathematical statements. After months of translating, he successfully translated all the words and digits. Unfortunately, due to the complexity of the language, he couldn’t figure out the exact number of ones in each number. All he knows is that they each have at least 2 ones and the first number (but not necessarily the second) has an even number of ones. Other than the ones, the only other digit is a single two. The following is the furthest he could translate it:

1…1 [with an even number of ones] is a prime number
1…12 is a prime number

Assuming both numbers use the same base number, prove that someone or something made a mistake.

  Submitted by Tristan    
Rating: 3.4000 (5 votes)
Solution: (Hide)
Assume no mistakes were made. First of all, the first number must be 11. If it were any longer it would be divisible by 11 and 10101...01. 11 can only be a prime number in an even base number. In an odd base number, 11 would be an even number, and could not be prime.

The problem appears in the second number. In an even base number, 1...12 must be an even number and cannot be prime.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
SolutionSOLUTIONAdy TZIDON2004-01-23 03:28:43
SolutionSolutionFederico Kereki2004-01-20 08:06:02
QuestionET?Richard2004-01-20 00:45:06
SolutionNo SubjectCharlie2004-01-19 14:21:12
SolutionShorte.g.2004-01-19 14:08:53
Solutionre: It looks to me like ...Gamer2004-01-19 14:08:48
Some ThoughtsIt looks to me like ...Richard2004-01-19 13:42:34
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