All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Numbers
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.

See The Solution Submitted by Tristan    
Rating: 3.4000 (5 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Solution | Comment 6 of 7 |
If the first number is more than two digits long, independently of the number base, you could write

111111....11 = 11 x 10101...1

so the number would be composite.

If the first number is two digits long, the number base could be either 1 (not possible, because then a "2" wouldn't be used in the second number) or a prime, greater than 2, minus 1, which works out to an even number.

In the latter case, call the base B; the second number would equal a multiple of B, + 2, which would be even, so it couldn't be a prime.
  Posted by Federico Kereki on 2004-01-20 08:06:02

Please log in:
Remember me:
Sign up! | Forgot password

Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (1)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information