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wu :: forums    riddles    medium (Moderators: william wu, SMQ, ThudnBlunder, Icarus, towr, Eigenray, Grimbal)    Combination « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Combination  (Read 519 times) mikedagr8 Uberpuzzler A rich man is one who is content; not wealthy.     Gender: Posts: 1105 Combination   « on: Oct 17th, 2007, 12:28am » Quote Modify Find 9 different integers from 1-20 inclusive such that no combination of any 3 of the 9 form an arithmetic progression. For example, if 2 integers chosen were 7 and 13, then that would preclude 1,10, and 19 from being included. « Last Edit: Oct 17th, 2007, 4:28am by mikedagr8 » IP Logged "It's not that I'm correct, it's that you're just not correct, and so; I am right." - M.P.E. gotit Uberpuzzler     Gender: Posts: 804 Re: Combination   « Reply #1 on: Oct 17th, 2007, 1:56am » Quote Modify I have found out 8 integers that satisfy the condition. They are 1,2,4,5,10,11,13 and 14. I am still working on the ninth. IP Logged All signatures are false. mikedagr8 Uberpuzzler A rich man is one who is content; not wealthy.     Gender: Posts: 1105 Re: Combination   « Reply #2 on: Oct 17th, 2007, 4:30am » Quote Modify on Oct 17th, 2007, 1:20am, Grimbal wrote: You meant 7 and 13? I did.     I have seen this done in two ways. I was able to solve it for only one of them. IP Logged "It's not that I'm correct, it's that you're just not correct, and so; I am right." - M.P.E. Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Combination   « Reply #3 on: Oct 17th, 2007, 6:58am » Quote Modify If you know one solution, the other is easy to find. bi = 21 - ai IP Logged mikedagr8 Uberpuzzler A rich man is one who is content; not wealthy.     Gender: Posts: 1105 Re: Combination   « Reply #4 on: Oct 17th, 2007, 2:28pm » Quote Modify What does that mean I'm guessing you either know both answers, or still working it out. IP Logged "It's not that I'm correct, it's that you're just not correct, and so; I am right." - M.P.E. FiBsTeR Senior Riddler     Gender: Posts: 581 Re: Combination   « Reply #5 on: Oct 17th, 2007, 2:53pm » Quote Modify He means that if you had one solution, then you could take each number and subtract them from 21 (essentially "reversing" the list starting at 20 and counting down), and you would end up with another solution. IP Logged Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Combination   « Reply #6 on: Oct 17th, 2007, 2:59pm » Quote Modify If you have one solution, say 1, 2, 4, 5, 10, 11, 13, 14 You can get a solution by taking it backwards, taking 21-x for each element x. 20, 19, 17, 16, 11, 10, 8, 7 Which is another solution for 6. Obviously, a, b, c are in a linear progression if and only if 21-a, 21-b, 21-c are. IP Logged pex Uberpuzzler     Gender: Posts: 880 Re: Combination   « Reply #7 on: Oct 17th, 2007, 3:16pm » Quote Modify Well, I have found the solutions - by complete enumeration, by lack of better alternatives that are apparent to me. (I tried to do it by hand, and found the same solution gotit mentioned for 8 numbers; but I couldn't get any further.)   hidden: We have as the only solutions   1, 2, 6, 7, 9, 14, 15, 18, 20   and its complement, as Grimbal noted,   20, 19, 15, 14, 12, 7, 6, 3, 1.   Edit: if someone finds a neater way to do this, I'm very interested... « Last Edit: Oct 17th, 2007, 3:17pm by pex » IP Logged mikedagr8 Uberpuzzler A rich man is one who is content; not wealthy.     Gender: Posts: 1105 Re: Combination   « Reply #8 on: Oct 18th, 2007, 1:44am » Quote Modify Those are the answers I had. I found mine by hand over the course of 2 gruelling hours . « Last Edit: Oct 18th, 2007, 1:45am by mikedagr8 » IP Logged "It's not that I'm correct, it's that you're just not correct, and so; I am right." - M.P.E. Grimbal wu::riddles Moderator Uberpuzzler     Gender: Posts: 7527 Re: Combination   « Reply #9 on: Oct 18th, 2007, 2:48am » Quote Modify My computer found them by hand over the course of 40 gruelling milliseconds.   IP Logged mikedagr8 Uberpuzzler A rich man is one who is content; not wealthy.     Gender: Posts: 1105 Re: Combination   « Reply #10 on: Oct 18th, 2007, 2:51am » Quote Modify on Oct 18th, 2007, 2:48am, Grimbal wrote: My computer found them by hand over the course of 40 gruelling milliseconds.   You're computer is obviously programmed a lot better than my 13 year old mine at the time  . Also I can only do one search at a time, not many thousands (I assume). IP Logged "It's not that I'm correct, it's that you're just not correct, and so; I am right." - M.P.E. 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