079

Part of 1966 All Russian Mathematical Olympiad

Problems(1)

ASU 079 All Russian MO 1966 three crossroads in a city

Source:

For three arbitrary crossroads

A,B,C

in a certain city there exist a way from

A

B

not coming through

C

. Prove that for every couple of the crossroads there exist at least two non-intersecting ways connecting them. (there are at least two crossroads in the city)