Art and Bill were sitting around the apartment they shared, playing one of their favorite drinking games--exchanging 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 1-6 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 various ways of using exponentiation, which doesn't require an added symbol--just superscripting. Here, I'll use the caret (^), but written out it's just superscripting:

Many ways involve wasting powers of 1, such as in

1^236 + 4 = 5
or
1^2^4^3 + 5 = 6
or
1^545 + 2 = 3
or
2 + 3 = 5^1^46
where it's understood the 1^46 is done before 5 to that power.

More satisfying is 2^5 + 4^1 = 36 or 5^1^6 + 4 = 3^2.

There's 1^2 + 4^3 = 65.

There are 240 variations the computer found (or 120 if you discount switching the order of the two addends).

Posted by Charlie on 2003-12-30 15:35:27