Can You Solve the 4-Digit Number Puzzle?

[eddybob123]

I challenge users to find a four digit number $\overline{abcd}$ that is equal to $a^a+b^b+c^c+d^d$. (Drunk)

 

[MarkFL]

I felt it was better to begin a new topic for this, especially since the other problem had not been solved yet. :D

 

[Albert1]

I challenge users to find a four digit number $\overline{abcd}$ that is equal to $a^a+b^b+c^c+d^d$. (Drunk)

Ans :$3435=3^3+4^4+3^3+5^5$
for $6^6=46656>9999$
$\therefore a,b,c,d \leq5$
$3^3=27$
$4^4=256$
$5^5=3125$
the next procedure is easy