Math Olympiad is called “Aoshu” in China. Aoshu is very popular in elementary schools. Nowadays, Aoshu is getting more and more difficult. Here is a classic Aoshu problem:
ABBDE __ ABCCC = BDBDE
In the equation above, a letter stands for a digit(0 – 9), and different letters stands for different digits. After you fill the blank with '+', '-', '×' or '÷', and replace the letters with digits, you get an equation.
How to make the equation right? Here is a solution:
12245 + 12000 = 24245
In that solution, A = 1, B = 2, C = 0, D = 4, E = 5, and '+' is filled in the blank.
When I was a kid, finding a solution is OK. But now, my daughter’s teacher tells her to find all solutions. That’s terrible. I doubt whether her teacher really knows how many solutions are there. So please write a program for me to solve this kind of problems.