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## Arnold and Carlos: Part 1

Math brain teasers require computations to solve.

 Puzzle ID: #32391 Fun: (2.7) Difficulty: (2.05) Category: Math Submitted By: HiImDavid

Arnold and Carlos love math puzzles. They are constantly making them up for each other to solve. One day, Arnold presents his friend Carlos with a problem. This problem has four clues. Here is the problem Arnold gave:

"I am thinking of a mystery number.

1. The mystery number is a 2-digit prime number.
2. When the digits of the mystery number are reversed, another 2-digit prime number is formed.
3. When the original number is added to the next highest prime number, the sum forms a square number.
4. When the mystery number is added to the 2nd prime number after it, the sum is evenly divisible by 4.

What is the mystery number?"

Can you help Carlos solve Arnold's problem?

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 goblu91 Aug 10, 2006 Easy............ scallio Aug 10, 2006 Very clever teaser... but I have to say it was NOT easy for me! My brain hurts! stil Aug 12, 2006 TOO MUCH INFORMATION! Good, but one could speed up the process by skipping clue #2. Beyond 2, every prime is odd, so the sum of the two primes in clue #3 will be even. The average of the two primes must be an integer which is half of a square number (and falls exactly between the two primes.) Odd squares produce fractions when halved, so they can be ignored. One tests the prime numbers preceding 18, 32, 50, 72, and 98. (These are the half values of 36, 64, 100, etc.) The result has 17, 47, and 71 as possiblities. Clue #4 eliminates both 47 and 71, making clue #2 extraneous.. stormtrooper Aug 12, 2006 Nice teaser. jennysugars Aug 14, 2006 Fun teaser! Good job! josty Aug 18, 2006 easy, i liked it, but it could have been more challenging Rishiaditya Aug 25, 2014 How can we include 23 in the list ?!!. Reverse 23 and we get 32 and it is not a prime number. This violates the second rule in the question.