superprismatic
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Everything posted by superprismatic
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Yes, I am sure. I checked all pairs of the 1344 and they all differ by at least 2. I tried to attach the file but it just sat there spinning a wheel -- nothing was uploaded. I tried the basic uploader, but I couldn't figure out how to use it -- there was no mention of uploading when I tried to use it.
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I'm very intrigued by this problem and I have no clue as to how to attack it. I'll be working on it and checking back frequently. I've tried to find info about such things on the web with no luck.
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Thanks, your modification is better than my solution. I just missed it!
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You said: "Then, X = root((k+1)(4k+3)/3) This means that 4k+3 must be a factor of 3; in turn, 4K must be a factor of 3" Why did you rule out that (k+1) might be a multiple of 3?
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Yes, I wrote my own,
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I wrote the program to exhaust over all numbers from 1234 to 9876543210
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My knee-jerk response is I'll have to write a program to see if this is the maximum.
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I thought it was pretty straightforward, so I didn't bother. But, since no one has tried yet, I'll give it another look and probably post my answer by tomorrow sometime.
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Prof. Templeton has a correct answer and psychic_mind has a good proof that 6 of each can't work. All that's left is to see how many ways you can place 5 queens and 5 knights on the board so that no piece attacks any other. Any takers for this?
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You can do better than 4 each!
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Consider a variant of the 8 Queens problem: you must place an equal number of knights and queens on a chessboard such that no piece attacks any other piece. What is the maximum number of pieces you can so place on the board, and how many different ways can you do it?
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41 = (((9+9+9)*(9+9+9))+9)/(9+9)
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No, that's not it.
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That's negative. The object is to find the smallest positive integer which cannot be expressed.
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I found this puzzle on the ITA Software web site. It is one of ITA's "retired" puzzles. The web site does not give the answer. I suppose the puzzle is difficult enough to require writing a program to solve it. I thought programming this was quite a little tricky but fun as well. I have an answer but bugs have been known to creep into my code. I hope you enjoy it. Here it is: Combining nine 9s with any number of the operators +, -, *, /, (, ) , what is the smallest positive integer that cannot be expressed? Hints: 1)The answer isn't zero. You can express zero like this: (9 - 9) * (9 + 9 + 9 + 9 + 9 + 9 + 9) Also, zero isn't a positive integer. 2)The answer isn't one. You can express one like this: 9 - (9 * 9 - 9)/9 + 9 - 9 + 9 - 9 3)It's not a trick question. 4)Be sure to handle parentheses correctly. Notes: 1)You cannot exponentiate. 2)You cannot concatenate (for example, put two 9s together to make 99). 3)The - operator can be used in either its binary or unary form. 4)Assume base 10.
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Your logic seems iron clad to me. I'm really interested in getting to the bottom of this. At the moment I'm in programming mode and it's hard to switch my mind to probabilities quickly. I'll mull it all over and get back to you if I get any ideas. This turned out to be a pretty interesting problem. Oddly enough, Tuckleton computed his (different from your) algorithm's success at precisely 15/27. I hope he (or someone else) jumps in and tries to explain this stuff.
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