KöMaL 2026 K884

A number is called a zigzag number if, when reading its digits from left to right, the second digit is smaller than the first, the third digit is larger than the second, the fourth digit is smaller than the third, and so on. Create all the zigzag numbers from digits $1$, $2$, $3$, $4$, $5$, i.e., all five-digit numbers $\overline{abcde}$ with all different digits satisfying $a>b$, $b<c$, $c>d$ and $d<e$. How many such five-digit zigzag numbers are there?