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wu :: forums    riddles    easy (Moderators: Icarus, towr, Eigenray, william wu, SMQ, ThudnBlunder, Grimbal)    Magic Hexagon « Previous topic | Next topic » Pages: 1  Reply Notify of replies Send Topic Print    Author  Topic: Magic Hexagon  (Read 2451 times) ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Magic Hexagon   MagicHexagon.gif « on: Jan 22nd, 2009, 6:23am » Quote Modify Insert the integers 1 to 19 in the circles below so that each of the horizontal and diagonal straight lines have the same sum. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Noke Lieu Uberpuzzler pen... paper... let's go! (and bit of plastic)     Gender: Posts: 1884 Re: Magic Hexagon   « Reply #1 on: Jan 26th, 2009, 5:50pm » Quote Modify If it helps...38 IP Logged a shade of wit and the art of farce. ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Magic Hexagon   « Reply #2 on: Jan 27th, 2009, 8:01am » Quote Modify Yeah, and the central number is 5, the same as the magic square of order 3.   It is not so difficult to prove that a magic hexagon of order 3 alone exists.   But solving it perhaps involves too much guesswork and too little Googling. IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Magic Hexagon   « Reply #3 on: Jan 27th, 2009, 8:07am » Quote Modify on Jan 27th, 2009, 8:01am, ThudanBlunder wrote: Yeah, and the central number is 5, the same as the magic square of order 3.   It is not so difficult to prove that a magic hexagon of order 3 alone exists.   But solving it perhaps involves too much guesswork and too little Googling. I'd have thought "too much programming" myself. 19! (or 18! if we take the middle number for granted) is tractable enough, especially with all the early cuts in the search tree. But meh. The effort to interestingness(?) ratio for that approach isn't attractive enough. « Last Edit: Jan 27th, 2009, 8:07am by towr » IP Logged Wikipedia, Google, Mathworld, Integer sequence DB ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Magic Hexagon   « Reply #4 on: Jan 27th, 2009, 8:14am » Quote Modify on Jan 27th, 2009, 8:07am, towr wrote: I'd have thought "too much programming" myself. 19! (or 18! if we take the middle number for granted) is tractable enough, especially with all the early cuts in the search tree. But meh. The effort to interestingness(?) ratio for that approach isn't attractive enough. I thought you were going to point out that a magic hexagon of order 1 exists, and indeed more than one if we consider rotations and reflections.   « Last Edit: Jan 27th, 2009, 9:53am by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. towr wu::riddles Moderator Uberpuzzler Some people are average, some are just mean.     Gender: Posts: 13730 Re: Magic Hexagon   « Reply #5 on: Jan 27th, 2009, 8:26am » Quote Modify on Jan 27th, 2009, 8:14am, ThudanBlunder wrote: I thought you were going to point that a magic hexagon of order 1 exists, and more than one if we consider rotations and reflections.   I don't even know what "magic X of order Y" means. So it would be disingenious of me to point such things out. IP Logged Wikipedia, Google, Mathworld, Integer sequence DB ThudnBlunder wu::riddles Moderator Uberpuzzler The dewdrop slides into the shining Sea     Gender: Posts: 4489 Re: Magic Hexagon   Magic_T_Hexagon.jpg « Reply #6 on: Jan 27th, 2009, 8:36am » Quote Modify on Jan 27th, 2009, 8:07am, towr wrote: I'd have thought "too much programming" myself. 19! (or 18! if we take the middle number for granted) is tractable enough, especially with all the early cuts in the search tree. Yeah, this magic T-hexagon was not discovered until 2003.   Interestingly, the sum of the numbers in the triangles pointing downwards equals the sum pointing upwards (150).     « Last Edit: Jan 27th, 2009, 10:36pm by ThudnBlunder » IP Logged THE MEEK SHALL INHERIT THE EARTH.....................................................................er, if that's all right with the rest of you. Noke Lieu Uberpuzzler pen... paper... let's go! (and bit of plastic)     Gender: Posts: 1884 Re: Magic Hexagon   magic_honeycomb.gif « Reply #7 on: Jan 27th, 2009, 1:55pm » Quote Modify on Jan 27th, 2009, 8:01am, ThudanBlunder wrote: But solving it perhaps involves too much guesswork and too little Googling.     wouldn't know. I have a physical copy of it on my desk... « Last Edit: Jan 27th, 2009, 2:25pm by Noke Lieu » IP Logged a shade of wit and the art of farce. mikedagr8 Uberpuzzler A rich man is one who is content; not wealthy.     Gender: Posts: 1105 Re: Magic Hexagon   magic_hexagon.JPG « Reply #8 on: Jan 27th, 2009, 6:01pm » Quote Modify Thought I'd finish off the half completed magic hexagon Noke started. Not much effort required. 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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