# Strong Numbers

**Discrete Mathematics**Level 4

An integer is called strong if it's decimal representation \(\overline { { a }_{ 1 }{ a }_{ 2 }{ a }_{ 3 }{ a }_{ 4 } } \) satisfies \({ a }_{ i }<{ a }_{ i+1 }\) if \(a_i\) is odd and \({ a }_{ i }>{ a }_{ i+1 }\) if \(a_i\) is even.

How many 4 digit strong numbers exist?

**Bonus:** how many 4 digit strong numbers have distinct digits?