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_ N D
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S _ N C _
B _ L L
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F _ T H _ R - _ N - L _ W ,
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S _ N C _
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( T H _
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K _ N Clue
Q1: ASK GOD B, "IF I ASKED YOU 'IS A RANDOM?', WOULD YOU SAY JA?". IF B ANSWERS JA, EITHER B IS RANDOM (AND IS ANSWERING RANDOMLY), OR B IS NOT RANDOM AND THE ANSWER INDICATES THAT A IS INDEED RANDOM. EITHER WAY, C IS NOT RANDOM. IF B ANSWERS DA, EITHER B IS RANDOM (AND IS ANSWERING RANDOMLY), OR B IS NOT RANDOM AND THE ANSWER INDICATES THAT A IS NOT RANDOM. EITHER WAY, YOU KNOW THE IDENTITY OF A GOD WHO IS NOT RANDOM. Q2: GO TO THE GOD WHO WAS IDENTIFIED AS NOT BEING RANDOM BY THE PREVIOUS QUESTION (EITHER A OR C), AND ASK HIM: "IF I ASKED YOU 'ARE YOU FALSE?', WOULD YOU SAY JA?". SINCE HE IS NOT RANDOM, AN ANSWER OF DA INDICATES THAT HE IS TRUE AND AN ANSWER OF JA INDICATES THAT HE IS FALSE. Q3: ASK THE SAME GOD THE QUESTION: "IF I ASKED YOU 'IS B RANDOM?', WOULD YOU SAY JA?". IF THE ANSWER IS JA, B IS RANDOM; IF THE ANSWER IS DA, THE GOD YOU HAVE NOT YET SPOKEN TO IS RANDOM. THE REMAINING GOD CAN BE IDENTIFIED BY ELIMINATION. SOURCE: WIKIPEDIA 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 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 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