Find the largest number, a single string of only digits  without radix or exponent, that can be equated to a mathematical expression that uses no variables and where each and every digit, 0 to 9, is used but once in the equation. Provide the equation.
Mathematical symbols and functions are permitted, yet limit each to less than the arbitrary number of ten.
If limited to digits 0 to 5, a possible answer, for example, could be:
5!/(4  3) = 120.
(In reply to
another  not quite right  answer by Leming)
Very good try.
If the notation, 4, was already recognized as a mathematical notation for 4.444444... it would meet the spirit of the problem.
I believe there are four notations for the repeating decimal, if you wish to use the notation. Either surround the repeating digit with a pair of parenthesis 0.(4), place an overline^{1} (called an vinculum) 0.4 over the repeating digits, or an overdot^{2} over the outermost repeating digit(s), or, if no other digits follow, follow the repeating digit with an ellipsis 0.4...
[ 1  the overline may not appear in all browsers; 2  I do not believe the overdot is yet supported by any major browser.]
Because there is notation that is not easily formed in a browser, defining an alternate notation for display in place of the original notation is acceptable, as long as the original notation meets the problem's requirements.
Edited on December 11, 2007, 12:55 pm

Posted by Dej Mar
on 20071211 12:44:02 