# Sum of five-digit number is 10 problem

So sum of five-digit number is 10. And all the digits are different from each other. If we sum this number with a number written in reversed order of those digits, we will get a number that has same digits. How many such five-digits numbers are there?

My attempt: I decomposed the five digit numbers to the powers of 10, and same with reverse number, but I am clueless what to do next. My hint is maybe that when I sum those two numbers highest one can get is a six-digit number and utilize it somehow?

• $1+2+3+4=10$ You need one more digit. Apr 18 '19 at 14:44

$$0+1+2+3+4=10$$ 0 can't be the first digit, so there are $$4\cdot4\cdot3\cdot2\cdot1=96$$ distinct, strictly 5 digit, numbers that use all the digits.