151

Part of 1971 All Soviet Union Mathematical Olympiad

Problems(1)

ASU 151 All Soviet Union MO 1971 (a-d)(b-c)<0 for some numbers in ring

Source:

Some numbers are written along the ring. If inequality

(a-d)(b-c) < 0

is held for the four arbitrary numbers in sequence

a,b,c,d

, you have to change the numbers

b

c

places. Prove that you will have to do this operation finite number of times.

combinatoricsalgebra