MathDB

076

Part of 1966 All Russian Mathematical Olympiad

Problems(1)

ASU 076 All Russian MO 1966 shortest path on cross-lined paper

Source:

6/19/2019
A rectangle ABCDABCD is drawn on the cross-lined paper with its sides laying on the lines, and ∣AD∣|AD| is kk times more than ∣AB∣|AB| (kk is an integer). All the shortest paths from AA to CC coming along the lines are considered. Prove that the number of those with the first link on [AD][AD] is kk times more then of those with the first link on [AB][AB].
algebra