T H _
S W _ T C H
W _ L L
B _
_ N
T H _
_ F F
P _ S _ T _ _ N .
A F T _ R
S W _ T C H _ N G
4
T _ M _ S ,
T H _
S W _ T C H
W _ L L
R _ T _ R N
T _
_ T S
_ R _ G _ N _ L
P _ S _ T _ _ N .
S _ ,
3 9 2 2
/
4
=
9 8 0
W _ T H
R _ M _ _ N D _ R
2 .
T H _
S W _ T C H
W _ L L
B _
_ T
M _ D _ _ M
P _ S _ T _ _ N
_ F T _ R
S W _ T C H _ N G
3 9 2 0
T _ M _ S ,
_ N D
_ T
_ F F
P _ S _ T _ _ N
_ F T _ R
_ N _ T H _ R
2
S W _ T C H _ S Clue
USE 4 HALF FILLED BARRELS TO FILL 2 EMPTY BARRELS. WE ARE THEN LEFT WITH 9 FULLY FILLED BARRELS, 3 HALF FILLED BARRELS AND 9 EMPTY BARRELS. EACH SON GETS 3 FULL BARRELS, 1 HALF-FULL BARREL, AND 3 EMPTY BARRELS NOMINATE ONE PRISONER WHO IS ALLOWED TO TURN THE LIGHT BULB OFF. THE REST OF THE PRISONERS ARE ALLOWED TO TURN ON THE LIGHT BULB IF THEY THEY HAVE NEVER TURNED IT ON BEFORE. IF THEY HAVE TURNED IT ON BEFORE THEY ARE NOT SUPPOSED TO FLIP THE SWITCH OR SAY ANYTHING. THE PRISONER THAT CAN TURN IT OFF THEN KNOWS THEY HAVE ALL BEEN THERE AND SAVES THEM ALL WHEN HE HAS TURNED IT OFF 99 TIMES YES. HE TOOK AS MUCH TIME FOR THE SECOND HALF OF HIS TRIP AS THE WHOLE TRIP WOULD HAVE TAKEN ON FOOT. SO NO MATTER HOW FAST THE TRAIN WAS, HE LOST EXACTLY AS MUCH TIME AS HE SPENT ON THE TRAIN. HE WOULD HAVE SAVED 1⁄30 OF THE TIME BY WALKING ALL THE WAY 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