Suppose you want to move from 0 to 100 on the number line. In each step, you either move right by a unit distance or you take a shortcut. A shortcut is simply a pre-specified pair of integers i , j with i < j.Given a shortcut i , j if you are at position i on the number line, you may directly move to j. Suppose T(k) denotes the smallest number of steps needed to move from k to 100. Suppose further that there is at most 1 shortcut involving any number, and in particular from 9 there is a shortcut to 15. Let y and z be such that T(9)= 1+ min (T(y),T(z)).
Then what is the value of the product yz ?
$y$ and $z$ are $10$ and $15$, because from $9$, you can move to $100$ via $10$ in $1+T(10)$ steps or via $15$ in $1+T(15)$ steps. Taking the minimum gives $T(9)=1+\min(T(10),T(15))$. Now, we have $yz=10\cdot 15=150$.
EDIT:
A problem like this is usually solved using Dynamic Programming. In this case, we calculate all $T(i)$ starting at $T(100)$ and going down to $T(0)$. It takes $0$ steps to reach $100$ from $100$, so $T(100)$ is $0$. It takes $1$ step from $99$, so $T(99)=1$. Now, if there is a bridge from $i$ to $j$ ($i<j$), then, from $i$ we can go to $i+1$ and to $j$. We know it takes $1+T(i+1)$ steps if we go via $i+1$ and $1+T(j)$ steps if we go via $j$. We take the minimum of those two because we want to minimize the total number of steps. Thus, $T(i)=1+\min(T(j),T(i+1))$. If you wanted, you could go down to $T(0)$ and calculate the minimal number of steps needed to go from $0$ to $100$.