Using two distinct signs (although 5 total), you can form 2011 with:
978 * 2 + 4 + 5 + 10 + 36 = 1956 + 55 = 2011
Using two distinct signs, and only 4 signs total, there are many solutions of the form:
a * b + c * d + e = 2011, my favorite being:
2 * 47 + 3 * 89 + 1650 = 2011, where a, b, c, and d are all prime
Using two distinct signs, and only 3 signs total, there are again many solutions of the form:
a * b + c + d = 2011, my favorite being:
3 * 287 + 509 + 641, where a, b, and d are all prime.
Finally, after testing numerous combinations of signs, I moved on to form a  b  c = 2011, and after finding that there were indeed solutions of this form, I decided to minimize the sum of a, b, and c to .
So, using one distinct sign, and only 2 signs total while minimizing (a + b + c):
2495  106  378 = 2011
That's the "best" solution that I can seem to come up with. Happy New Year everyone!

Posted by Justin
on 20110101 13:29:41 