Turkey Junior Olympiad 1999, Part II - P2
Source:
January 18, 2013
Problem Statement
Each of integers from to 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 .[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]