Digit Substitution

Computer Science Level 3

Each letter in the following equation can be replaced with a unique digit 0 through 4 such that the statement holds true in base 5.

\((abcde)(edcba)={aaaaaddcbe} \)

If each letter is replaced with the unique digit that makes the above statement true, what is the value of \(aaaaaddcbe\) converted to base 10?

Note: An example of substitution would be setting \(a=4, b=3, c=2, d=1, e=0\). This turns the equation into \((43210)(01234)=4444411230\) (which, I might add, is not a true statement in base 5).


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