I thought this was a theorem of John Conway's but I can't find a reference to convince me that my memory is correct. --Joshua Zucker On Mon, Jul 19, 2010 at 1:58 PM, Erich Friedman <efriedma@stetson.edu> wrote:
this is actually a variant of an old puzzle, with 4 replaced by 3. they are equivalent problems since 4 can be done from 3 and 3 from 4.
every number up to 196 has such a representation. i'm guessing all numbers do.
erich
On Jul 19, 2010, at 4:12 PM, Marc LeBrun wrote:
Can every integer be represented by a composition of integer square root ($) and factorial (!) applied to 3?
Some example representations: 3 = 3 6 = 3! 1 = 3$ 2 = 3!$ 720 = 3!! 26 = 3!!$ 5 = 3!!$$ 120 = 3!!$$! 10 = 3!!$$! ...
If not, what is the smallest counterexample?
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