Given an equation such as

ABCD + BDC = EAEA

one can replace each letter with a digit (0-9) in order to come to a correct solution. That is, you'll replace all the As with one digit, all the Bs with another, and so on. Two distinct letters will not map to the same digit. A leading digit in a term will not map to 0.

Your code must create the function calculate(left, operation, right, answer), which will be called multiple times and should print (to stdout) answers in the following format:

calculate("ABCD", "+", "BDC", "EAEA")

1538 + 583 = 2121
1547 + 574 = 2121
1574 + 547 = 2121
1583 + 538 = 2121
3658 + 685 = 4343
3685 + 658 = 4343

The letters used will be uppercase letters from A to Z. Numbers may also be intermixed in the given arguments, which should not be replaced.

Operations can be one of * (multiplication), + (addition), - (subtraction), ^ (exponentiation), or ?. If it is ?, then it can be any one of *, +, -, or ^ and all should be tried (and the correct operation printed for each one).

Your results should be sorted.

Bad data will not be fed into the function, so error checking on input is not necessary.

More examples

calculate("AA", "+", "BC", "100")

11 + 89 = 100
22 + 78 = 100
33 + 67 = 100
44 + 56 = 100
66 + 34 = 100
77 + 23 = 100
88 + 12 = 100

calculate("XYZ", "+", "XY", "6QQ")

546 + 54 = 600
576 + 57 = 633
586 + 58 = 644

calculate("X", "?", "X", "Y")

1 + 1 = 2
2 * 2 = 4
2 + 2 = 4
2 ^ 2 = 4
3 * 3 = 9
3 + 3 = 6
4 + 4 = 8

calculate("AAAAAAAA", "+", "B", "C") <<code>><</code>> (no output printed)

Prize

A ticket to BlizzCon 2009. You must be at least 18 years of age in order to participate in this contest. If you participate in another contest on WowAce/CurseForge for a BlizzCon 2009 ticket, you will only be able to redeem one. You must use the ticket for yourself or you may gift it to another author (i.e. not just your girlfriend), not for resale. We will not be paying travel costs. You must be an author on either CurseForge or WowAce to participate.

Runners-up will receive 500 Curse Points or 1 year of free Curse Premium of a user of your choosing. If you choose to opt out of a BlizzCon ticket, you may still be a Runner-up.

Other info

We have the right to revoke your right to participate at any time.

Your submission must be completely your own work, you're free to use resources to figure out how you would code the solution, as long as all the code is your own.

Your submission must run in Lua 5.1.4, in a standalone environment (not in WoW). You cannot use any external libraries outside of what Lua itself provides.

Winners

Alphabet Mathematics solution v1, Jacob Dlougach. by Dlougach

Very clean implementation, and the use of coroutines in order to generate permutations was a nice way of handling it.

Shefki's Entry by Shefki

Very clean and well-documented