B _ L L
_ S
T H _
Q _ _ R T _ R B _ C K ,
K _ N
_ S
T H _
R _ C _ _ V _ R ,
_ N D
M _ R K
_ S
T H _
K _ C K _ R .
S _ N C _
B _ L L
_ S
K _ N ' S
F _ T H _ R - _ N - L _ W ,
B _ T H
B _ L L
_ N D
K _ N
M _ S T
B _
M _ R R _ _ D .
T H _ S
L _ _ V _ S
T H _
_ N L Y
R _ M _ _ N _ N G
P _ R S _ N ,
M _ R K ,
T _
B _
T H _
B _ C H _ L _ R
( _ N D
H _ N C _
T H _
K _ C K _ R ) .
S _ N C _
B _ L L
_ S
T _ L L _ R
T H _ N
T H _
R _ C _ _ V _ R ,
B _ L L
M _ S T
N _ T
B _
T H _
R _ C _ _ V _ R .
B Y
P R _ C _ S S
_ F
_ L _ M _ N _ T _ _ N ,
W _
C _ N C L _ D _
T H _ T
B _ L L
_ S
T H _
Q _ _ R T _ R B _ C K .
T H _
R _ M _ _ N _ N G
P _ S _ T _ _ N
( T H _
R _ C _ _ V _ R )
G _ _ S
T _
K _ N Clue
THE CORRECT BUTTON IS FIFTH FROM THE LEFT. THE INSCRIPTION STATES THAT ONLY ONE OF THE SIX BUTTONS IS NOT MENTIONED, SO EXACTLY FIVE DIFFERENT BUTTONS ARE MENTIONED. IN THE STATEMENT OF RELATIONS BETWEEN POSITIONS, THE INSCRIPTION REFERS TO SIX BUTTONS; HOWEVER, THE FIRST AND LAST MENTIONED BUTTONS ARE THE SAME ONE. ONE NOW LABELS THE BUTTONS MENTIONED IN THE INSCRIPTION IN THE ORDER A B C D E A AND BEGINS BY NOTING THE MOST PRECISE RELATION, THAT IS, B IS THREE TO THE RIGHT OF C. SINCE NO POSITION MAY HAVE TWO LETTERS, OUR DEDUCTIONS SHOW THAT FROM LEFT TO RIGHT THE BUTTONS ARE D E C A ? B. SO THE CORRECT BUTTON MUST BE THE MISSING ONE NO ONE IS TALLER, BOTH ARE SAME AS A AND B ARE THE SAME PERSON. AS IT IS MENTIONED THAT 500 MEN ARE ARRANGED IN AN ARRAY OF 10 ROWS AND 50 COLUMNS ACCORDING TO THEIR HEIGHTS. LET'S ASSUME THAT POSITION NUMBERS REPRESENT THEIR HEIGHTS. HENCE, THE SHORTEST AMONG THE 50, 100, 150, ... 450, 500 IS PERSON WITH HEIGHT 50 I.E. A. SIMILARLY THE TALLEST AMONG 1, 2, 3, 4, 5, ..... 48, 48, 50 IS PERSON WITH HEIGHT 50 I.E. B. NOW, BOTH A AND B ARE THE PERSON WITH HEIGHT 50. HENCE BOTH ARE THE SAME THE SWITCH WILL BE IN THE OFF POSITION. AFTER SWITCHING 4 TIMES, THE SWITCH WILL RETURN TO ITS ORIGINAL POSITION. SO, 3922 / 4 = 980 WITH REMAINDER 2. THE SWITCH WILL BE AT MEDIUM POSITION AFTER SWITCHING 3920 TIMES, AND AT OFF POSITION AFTER ANOTHER 2 SWITCHES BILL IS THE QUARTERBACK, KEN IS THE RECEIVER, AND MARK IS THE KICKER. SINCE BILL IS KEN'S FATHER-IN-LAW, BOTH BILL AND KEN MUST BE MARRIED. THIS LEAVES THE ONLY REMAINING PERSON, MARK, TO BE THE BACHELOR (AND HENCE THE KICKER). SINCE BILL IS TALLER THAN THE RECEIVER, BILL MUST NOT BE THE RECEIVER. BY PROCESS OF ELIMINATION, WE CONCLUDE THAT BILL IS THE QUARTERBACK. THE REMAINING POSITION (THE RECEIVER) GOES TO KEN