25 May
2005
25 May
'05
11:28 a.m.
a(n) = minimum value of k so that k copies each of cubes of sides 1 through n can be used to exactly fill some rectangular box.
is it obvious that such k exists?
sure. let L = lcm(1, 2, ... n) and S=(n)(n+1)(2n+1)/6. then cubes of every side 1 <= i <= n can fill a i x L x L slab, and you can put these slabs together to form an S x L x L box, so a(n) <= L^2. [mike, are you driving up for the UCF vs. stetson baseball game tonight?] erich