6
$\begingroup$

$Given$:

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.

$\endgroup$
7
$\begingroup$

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:

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

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.