Problems(2)
Cities and airlines
Source: St Petersburg Olympiad 2012, Grade 11, P7
9/29/2017
Some cities of Russia are connected with some cities of Ukraine with international airlines. The Interstate Council for the Promotion of Migration intends to introduce a one-way traffic on each airline so that, by taking off from the city, it could no longer be returned in this city (using other one-way airlines). Prove that the number of ways to do this is not divided by .
combinatoricsgraph theory
Breaking sticks
Source: St Petersburg Olympiad 2012, Grade 9, P7
9/29/2017
We have sticks with integer length, and sum of length is . We need to have sticks with lengths . For it we can break some sticks ( for example from stick with length we can get and ).
For what minimal it is always possible?
combinatoricsnumber theory