Digit Substitution

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.

( a b c d e ) ( e d c b a ) = a a a a a d d c b e (abcde)(edcba)={aaaaaddcbe}

If each letter is replaced with the unique digit that makes the above statement true, what is the value of a a a a a d d c b e aaaaaddcbe converted to base 10?

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


The answer is 2442148.

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