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Jul 26th, 2012, 10:30 AM
#17
Re: Interesting math problems
Well, that goes along the second to last category, of disprovable (or alternatively, (dis)provable by contradiction). In this case, however, that's not a trivial matter. Even if you find a number that is not constructable, it takes some skill to formally prove that it is not constructable (kind of like proving that a compass and straight edge cannot construct every angle in finite time).
I spent some time doodling this problem out last night, and constructed everything from 1-180 to pick up patterns. If there are non-constructable numbers, I suspect the first will be near a value n!/2. For example, 348 is near 6!/2, and that is a number that I haven't been able to construct yet.
Last edited by Lenggries; Jul 26th, 2012 at 11:30 AM.
Reason: 348 = (0! + 1!)(5! + (4! * 2!) + 3!)... stupid arithmatic mistake
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