# (Bulgarian OI) You are given a matrix A with n rows and m columns. An cell is considered a local minimum if it’s row and column neighbours have higher values. One query is what is the value of A[i][j]. Find a local minimum in as few queries as possible.
# (folklore) A celebrity in a group of n people is a person that is known by everybody but doesn’t know anybody. Given a group of n people you can query if person x knows person y. Using the fewest number of queries possible, find out if there’s a celebrity in that group.
# (CLRS) Professor Diogenes has n supposedly identical integrated-circuit chips that in principle are capable of testing each other. The professor’s test jig accommodates two chips at a time. When the jig is loaded, each chip tests the other and reports whether it is good or bad. A good chip always reports accurately whether the other chip is good or bad, but the professor cannot trust the answer of a bad chip. Thus, the four possible outcomes of a test are as follows:

| Chip A says | Chip B says | Conclusion |
| B is good | A is good | both are good, or both are bad |

|Chip A says | Chip B says | Conclusion|
|B is good | A is good | both are good, or both are bad|

|B is good | A is bad | at least one is bad|
|B is bad | A is good | at least one is bad|
|B is bad | A is bad | at least one is bad|