MathDB

2

Part of 1999 Turkey Junior National Olympiad

Problems(1)

Turkey Junior Olympiad 1999, Part II - P2

Source:

1/18/2013
Each of integers from 11 to 2020 are placed into the dots below. Two dots are adjacent, if below figure contains a line segment connecting them. Prove that how the numbers are arranged, it is possible to find an adjacent pair such that the difference between the numbers written on them is greater than 33.
[asy]
real u=0.25cm; for(int i = 0; i < 4; ++i) { real v = u*(i+1); pair P1 = dir(90+0*72)*(0,v); pair P2 = dir(90+1*72)*(0,v); pair P3 = dir(90+2*72)*(0,v); pair P4 = dir(90+3*72)*(0,v); pair P5 = dir(90+4*72)*(0,v); dot(P1);dot(P2); dot(P3);dot(P4);dot(P5); path p = P1--P2--P3--P4--P5--cycle; draw(p); } [/asy]