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<blockquote data-quote="Pielorinho" data-source="post: 1348798" data-attributes="member: 259">Corran, I do hope you're right, because your reasoning (minus the computer work) were as far as I was able to take the problem over the weekend. I'm not a programmer, so I couldn't figure out how to throw a CPU at the problem; short of figuring out every number P, I was going to have to throw up my hands.&nbsp;I'll make one minor adjustment to the way you stated property P:&nbsp; a number with property P is neither the sum of two primes NOR the sum of a prime and its square.&nbsp; Twelve, for example, is the sum of three and nine, and is thereby disqualified; if A had been given twelve, then B could have been given 27, and 27 may only be factored into 3 and 9.&nbsp; Even though nine isn't a prime number, there's no other two integers greater than 1 that can be multiplied to equal 27.&nbsp;This is a very minor adjustment, for two reasons.&nbsp; First, there's only four numbers that are thereby disallowed:&nbsp; 6 (2 and 4), 12 (3 and 9), 30 (5 and 25), and 56 (7 and 49).&nbsp; Second, all these pairs can be disqualified by other means:&nbsp; 6 is disqualified by 3 and 3 (assuming X and Y can be the same number), 12 by 5 and 7, 30 by 13 and 17, and 56 by 43 and 13.&nbsp;Still, it's an interesting quirk to the problem.&nbsp;Daniel</blockquote>

[QUOTE="Pielorinho, post: 1348798, member: 259"] Corran, I do hope you're right, because your reasoning (minus the computer work) were as far as I was able to take the problem over the weekend. I'm not a programmer, so I couldn't figure out how to throw a CPU at the problem; short of figuring out every number P, I was going to have to throw up my hands. I'll make one minor adjustment to the way you stated property P: a number with property P is neither the sum of two primes NOR the sum of a prime and its square. Twelve, for example, is the sum of three and nine, and is thereby disqualified; if A had been given twelve, then B could have been given 27, and 27 may only be factored into 3 and 9. Even though nine isn't a prime number, there's no other two integers greater than 1 that can be multiplied to equal 27. This is a very minor adjustment, for two reasons. First, there's only four numbers that are thereby disallowed: 6 (2 and 4), 12 (3 and 9), 30 (5 and 25), and 56 (7 and 49). Second, all these pairs can be disqualified by other means: 6 is disqualified by 3 and 3 (assuming X and Y can be the same number), 12 by 5 and 7, 30 by 13 and 17, and 56 by 43 and 13. Still, it's an interesting quirk to the problem. Daniel [/QUOTE]

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