4 True/False Statements on a Card
Source: 1978 AHSME #22
May 18, 2014
AMC
Problem Statement
The following four statements, and only these are found on a card:
[asy]
pair A,B,C,D,E,F,G;
A=(0,1);
B=(0,5);
C=(11,5);
D=(11,1);
E=(0,4);
F=(0,3);
G=(0,2);
draw(A--B--C--D--cycle);
label("On this card exactly one statement is false.", B, SE);
label("On this card exactly two statements are false.", E, SE);
label("On this card exactly three statements are false.", F, SE);
label("On this card exactly four statements are false.", G, SE);
[/asy]
(Assume each statement is either true or false.) Among them the number of false statements is exactly