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Message: <blockquote data-quote="Tiefling" data-source="post: 1345953" data-attributes="member: 251">I got the same answer as everyone else, using the following algorithm:[spoiler]Equation of Death - # of Killings to Go at the End - Highest Remaining # at the End - Calibration Number(Calibration Number is 0 if the first remaining number in the next round will be killed, 1 if the second remaining number in the next round will be killed.)1+n*2 - 499 - 1000 - 02+n*4 - 249 - 1000 - 04+n*8 - 124 - 1000 - 08+n*16 - 61 - 992 - 132+n*32 - 30 - 976 - 148+n*32 - 0 - 976 - N/AIn which n is and integer on [0,Previous Remaining Killings Minus One]. Each line can be arrived at by taking the previous line and performing some simple logic and arithmetic. Crude, I know, but it works and takes about 5 minutes.[/spoiler]Concerning the 52 card problem-[spoiler]Take 13 cards from the deck to form the second pile, and flip them all over. If you subtract x turned cards from the first pile it has 13-x turned cards. Since the second pile had 13-x rightside-up cards, it now has 13-x turned cards. Equal.[/spoiler]Concerning the Evil Villain, Secret Numbers problem-[spoiler]Poor villain. He managed to A) imprison two lightning-fast number theorists and B) pick exactly the wrong pair of numbers.This problem requires that a few ground rules be laid out to determine the validity of a pair of numbers. But first, let me define a few terms for this problem: a "sumoid" is any pair of numbers whose sum is a desired number. A "productoid" is any pair of numbers whose product is a desired number. A sumoid of a productoid is a sumoid of the number that the productoid pair adds to. A productoid of a sumoid is a productoid of the number that the sumoid pair multiplies to. Whew!1. A and B cannot both be prime, for obvious reasons.2. None of the sumoids of A can be both prime, as Person A could not be sure that it was a false sumoid and/or that Person B could not factor it.3. [For every false productoid of B, there must be at least one sumoid of that productoid that is a pair of prime numbers. This cannot apply to the true productoid of B.] This allows Person B to eliminate those false productoids upon hearing that Person A knew he could not factor B, leaving only the true productoid, (X,Y).4. Rule 3 does not apply to any of the false sumoids of A. That is, if you have a false sumoid (c,d) then either zero or two or more of its productoids lack any prime sumoids, but never exactly one. This allows Person A to locate the false sumoids of A when informed of Person B's success.This could also be written as follows:1. X and Y are both integers on [2,99]2. X /= prime OR Y /= prime3. X+Y = A4. X*Y = B5. A-q /= prime OR q /= prime where q is any integer on [2,A-2]6. B/C = D where C is any integer on [2,B/2] EXCEPT X or Y7. C+D-q = prime AND q = prime for at least one integer q on [2,C+D-2]8. E(A-E) = F where E is any integer on [2,A-2] EXCEPT X or Y9. F/G = H where G is any divisor of F on [2,F/2]10.G+H-q = prime and q = prime for either ZERO or TWO OR MORE possible integers q on [2,G+H-2]So the sequence goes like this:1. Person A finds that none of the sumoids of A are both prime, meaning that Person B could not possibly factor B into its true productoid without more information.2. Person B finds that one of B's productoids has a sum with no prime sumoids, while all the other productoids have at least one such sumoid.3. Person A tells Person B that Person B could not have found the answer.4. Person B deduces that only the productoid with a sum producing no prime sumoids could be correct, as all the others would lead to uncertainty in Person B. He announces his success.5. Person A figures out what Person B deduced, and finds that it only works on the sumoid of A that correspond to with Rule 3, not those that correspond to Rule 4. He determines what the true sumoid is, and also announces his success.The rules allow a program to be written for or a bored mathematician to be prodded into examining each of the 9604 possible combinations in turn until finding one that works. But I'm not about to try.[/spoiler]</blockquote>

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