$Given$:
C, I, L, U, V are all distinct digits and can vary from 0 to 9.
$LIV$, $UVC$ are concatenated Numbers.
$U^U$ + $V^U$ + $C^U$ = $UVC$
$L^U$ + $I^U$ + $V^U$ = $LIV$
Solve for all the digits.
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1 Answer
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0
Immediately,
The first line includes a digit raised to itself, summed with two other numbers that resulted in a three digit number (beginning with that digit). This immediately ruled out anything above $4^4$ as $5^5 > 599$. $U = 0,1,2$ was impossible as even the highest possible sum, $2^2 + 8^2 + 9^2$ is less than $200$. So U was either 3 or 4. $U = 4$ was impossible, as $5^4 > 499$ and $4^4 + 3^4 + 2^4 < 400$, leaving no possible way to reach a number with the required first digit. So $U = 3$. The rest fell into place via trial and error.
$C, I, L, U, V =$
$1, 0, 4, 3, 7$
Equations:
$3^3 + 7^3 + 1^3 = 27 + 343 + 1 = 371$
$4^3 + 0^3 + 7^3 = 64 + 0 + 343 = 407$
