Sergeants and solders
Source: All-Russian Olympiad 1996, Grade 10, Second Day, Problem 6
April 18, 2013
inductioncombinatorics proposedcombinatorics
Problem Statement
Three sergeants and several solders serve in a platoon. The sergeants take turns on duty. The commander has given the following orders:
(a) Each day, at least one task must be issued to a soldier.
(b) No soldier may have more than two task or receive more than one tasks in a single day.
(c) The lists of soldiers receiving tasks for two different days must not be the same.
(d) The first sergeant violating any of these orders will be jailed.
Can at least one of the sergeants, without conspiring with the others, give tasks according to these rules and avoid being jailed?M. Kulikov