Art and Bill were sitting around the apartment they shared, playing one of their favorite drinking gamesexchanging math problems.
Bill wrote down on a piece of paper the equation below, and told Art to fill in the blanks only using each of the digits 16 only once, to make a valid equation.
"Easy enough," said Art, picking up a pencil. After a few minutes of wracking his head, however, he was sure Bill had had a few too many. Bill insisted he hadn't, and there is actually more than one way to do it, to which Art threw up his hands in defeat.
How many ways can you find to fill in this equation using the digits one through six, once each?
___ + ___ = ___
There are more than 900 ways to fill in the blanks in the equation ___ + ___ = ___ with the digits one through six, once each.
The large number of possibilities are through the use of exponentiation, the use of tetration, and the use of bases (radix), as well as recognizing the commutative law of addition (a+b = b+a).
Examples:
31_{6} + 5 = 24
1^{4} + 35 = 6^{2}
^{2}1 + 4^{3} = 65
Edited on October 28, 2011, 10:43 pm

Posted by Dej Mar
on 20090612 23:22:41 