Question 133
There are $100$ doors labeled with numbers $1, 2, \ldots, 100$. You have $100$ keys labeled with numbers. Each key corresponds to exactly one door. If the key $i$ corresponds to the door $j$, then $|i - j| \le 1$. At each turn, you may pick doors with numbers $i$ and $j$ and check whether the key $i$ corresponds to the door $j$. Can you find which key corresponds to which door in
a) $99$ turns?
b) $75$ turns?
c) $74$ turns?
a) $99$ turns?
b) $75$ turns?
c) $74$ turns?