5
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$Given$:

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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6
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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:

$3^3 + 7^3 + 1^3 = 27 + 343 + 1 = 371$
$4^3 + 0^3 + 7^3 = 64 + 0 + 343 = 407$

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  • $\begingroup$ Explain the logic $\endgroup$ – Uvc Jun 12 at 19:17
  • $\begingroup$ @Uvc What logic? Does the math not speak for itself? $\endgroup$ – scatter Jun 12 at 19:18
  • 2
    $\begingroup$ Usually, for this kind of puzzles, deductive reasoning has to be given how you arrived at the final solution $\endgroup$ – Uvc Jun 12 at 19:19
  • $\begingroup$ That’s much better $\endgroup$ – Uvc Jun 12 at 19:30

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