superprismatic
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Everything posted by superprismatic
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No, it isn't correct. Sorry.
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Two players, A and B, play the following game: Each secretly chooses a real number and passes his choice to a judge. Neither A nor B gets to see the other's choice of number. The judge then multiplies the two numbers and reveals the most significant (non-zero) digit of the result. If this digit is 1, 2, or 3, player A wins $1 and B wins nothing. If this digit is 4, 5, 6, 7, 8, or 9, player B wins $1 and A wins nothing. If they play N games, each using an optimal strategy, what is the expected winnings for each player? Why?
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araver, bartf, and dark_magician_92 all solved it.
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duke2cool: I think we both misunderstand what AZ is thinking. Taking his example in post #5, A and B are friends, B and F are friends, but A and F are enemies. So, two of B's friends are enemies. I don't think a solution is possible because everyone on the island may be friends with everyone else. In that case, a solution is impossible because there simply are no enemies. So, some assumptions about the friend/enemy makeup of the island must be made in order for a solution to exist.
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I must not understand something. Is it not possible that every pair of persons on the island are enemies? In which case there is no solution to the problem. Perhaps you have some unspecified rules about enemy/friend relationships.
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You are correct that the hat layout of 0000011000 is a loser. I specified the only winning layouts when I said "There are 14 winning 10-long hat assignments which win using this strategy. They are 0000000000 0011100111 0101010101 0101101011 0110101101 0111001110 1001110011 1010101010 1010110101 1011010110 1100111001 1101011010 1110011100 1111111111". This is 14 winners out of 128 possibilities. All the others are losers. I hope this helps you understand my strategy. By the way, I ran my program a bit longer and I got a much better score of 24 out of 128. But this doesn't help in the understanding of what I did.
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Do you have an 'Ah-Ah' solution? I'd like to see it, if you don't mind explaining it. I enjoyed the nice 'Ah-Ah' you had for your 12 friends problem. I just solved this Christmas problem with a boring old discrete hill-climb.
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I'm thinking of a polynomial P(x) which has non-negative integer coefficients. Now, P(1)=14 and P(15)=5296846548. What is the polynomial, P(x), of which I think? Please use spoilers.
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Please tell me how to put an attached image into a spoiler like you did here. I tried to do it for my last post but I couldn't figure it out. Thanks.
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What happens if everyone abstains? Play again? Lose?
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That rank is purely a reflection of the number of posts. So, it's really is a measure of activity. I wouldn't worry about it if I were you. I've seen NEWBIEs around here who are obviously PhDs in math related topics. I've also seen teenagers who are advanced members. Most of us just love math and logic problems. That's the main thing around these here parts, partner!
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Look at which explains it.
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