Problem of the Week-2

11 scientists are working on a secret project. They wish to lock up the documents in a cabinet so that the cabinet can be opened if and only if six or more of the scientists are present. What is the smallest number of locks needed? What is the smallest number of keys to the locks each scientist must carry?

Carefully explain your answer. An answer without a valid combinatorial justification does not receive credit.

Submit your solution to Noah Aydin, RBH 309-A (e-mail: aydinn@kenyon.edu) by 5 pm on February 14.