AMC 8 2003 Problem 18
Source:
July 23, 2011
AMCAMC 8
Problem Statement
Each of the twenty dots on the graph below represents one of Sarah's classmates. Classmates who are friends are connected with a line segment. For her birthday party, Sarah is inviting only the following: all of her friends and all of those classmates who are friends with at least one of her friends. How many classmates will not be invited to Sarah's party?
[asy]/* AMC8 2003 #18 Problem */
pair a=(102,256), b=(68,131), c=(162,101), d=(134,150);
pair e=(269,105), f=(359,104), g=(303,12), h=(579,211);
pair i=(534, 342), j=(442,432), k=(374,484), l=(278,501);
pair m=(282,411), n=(147,451), o=(103,437), p=(31,373);
pair q=(419,175), r=(462,209), s=(477,288), t=(443,358);
pair oval=(282,303);
draw(l--m--n--cycle);
draw(p--oval);
draw(o--oval);
draw(b--d--oval);
draw(c--d--e--oval);
draw(e--f--g--h--i--j--oval);
draw(k--oval);
draw(q--oval);
draw(s--oval);
draw(r--s--t--oval);
dot(a); dot(b); dot(c); dot(d); dot(e); dot(f); dot(g); dot(h);
dot(i); dot(j); dot(k); dot(l); dot(m); dot(n); dot(o); dot(p);
dot(q); dot(r); dot(s); dot(t);
filldraw(yscale(.5)*Circle((282,606),80),white,black);
label(scale(0.75)*"Sarah", oval);[/asy]