(In reply to re: Initial thoughts.
I disagree with three things in this:
"For a given set of numbers, 0 through 2010, that add up to 2010 the
representation is 4 x's interspersed among 2010 + signs if starting from
zero. That's C(2014,4) = 683,489,813,501, which would be the answer if
the base were a prime number, such as 2 or 5, rather than the 10 that it
If anything it would be C(2010,3). There are 2010 + signs, you are choosing which three to change to *, which would create your four exponents.
It doesnt account for numbers in increasing order of magnitude.
It also doesnt account for keeping the numbers distinct.
Using a smaller example: 2^8 can only be broken into four distinct positive integers arranged in increasing order of magnitude in two ways:
Posted by Jer
on 2011-03-21 14:07:59