T H _
P R _ B _ B _ L _ T Y
_ F
T H _
_ N T S
C _ L L _ D _ N G
_ S
0 . 7 5 .
E _ C H
_ N T
C _ N
M _ V _
_ N
2
D _ F F _ R _ N T
D _ R _ C T _ _ N S .
B _ C _ _ S _
T H _ R _
_ R _
3
_ N T S ,
T H _ S
M _ _ N S
T H _ T
T H _ R _
_ R _
2 3
( 8 )
P _ S S _ B L _
W _ Y S
T H _ T
T H _
_ N T S
C _ N
M _ V _ .
N _ W ,
T H _ R _
W _ L L
N _ V _ R
B _
_
C _ L L _ S _ _ N
B _ T W _ _ N
_ N Y
_ F
T H _
_ N T S
_ F
T H _ Y
_ R _
_ L L
W _ L K _ N G
_ N
T H _
S _ M _
D _ R _ C T _ _ N .
A N D ,
T H _
_ N L Y
T _ M _
T H _ Y
W _ L L
B _
W _ L K _ N G
_ N
T H _
S _ M _
D _ R _ C T _ _ N
_ S
_ F
T H _ Y
_ R _
_ L L
W _ L K _ N G
_ _ T H _ R
C L _ C K W _ S _
_ R
C _ _ N T _ R - C L _ C K W _ S _
_ R _ _ N D
T H _
T R _ _ N G L _ .
S _ ,
T H _ R _
_ R _
_ N L Y
T W _
S C _ N _ R _ _ S
_ N
W H _ C H
_
C _ L L _ S _ _ N
W _ L L
N _ T
H _ P P _ N
B _ T W _ _ N
T H _
_ N T S .
T H _ S
M _ _ N S
T H _ T
T H _ R _
_ R _
6
S C _ N _ R _ _ S
W H _ R _
T H _
_ N T S
W _ L L
C _ L L _ D _ .
A N D
6
_ _ T
_ F
8
P _ S S _ B L _
S C _ N _ R _ _ S ,
M _ _ N S
T H _ T
T H _
P R _ B _ B _ L _ T Y
_ F
C _ L L _ S _ _ N
_ S
6 / 8 ,
W H _ C H
_ Q _ _ L S
3 / 4
_ R
0 . 7 5 .
T H _ S ,
T H _
P R _ B _ B _ L _ T Y
_ F
T H _
_ N T S
C _ L L _ D _ N G
_ S
0 . 7 5 Clue
THE ELDEST IS 9 YEARS OLD AND THE 2 YOUNGER ONES ARE 2 YEARS OLD. LET'S BREAK IT DOWN. THE PRODUCT OF THEIR AGES IS 36. SO THE POSSIBLE CHOICES ARE: 1,1,36 - SUM(1,1,36) = 38 1,6,6 - SUM(1,6,6) = 13 1,2,18 - SUM(1,2,18) = 21 1,3,12 - SUM(1,3,12) = 16 1,4,9 - SUM(1,4,9) = 14 2,2,9 - SUM(2,2,9) = 13 2,3,6 - SUM(2,3,6) = 11 3,3,4 - SUM(3,3,4) = 10 SIX OF THE SUMS ARE UNIQUE, SO IF IT WERE ONE OF THOSE, TOM WOULD HAVE RECOGNISED THE NUMBER ACROSS THE STREET THAT MATCHES AND HE WOULD KNOW THE ANSWER, BUT HE COULD NOT FIGURE OUT THE ANSWER. THIS MEANS THERE ARE TWO OR MORE COMBINATIONS WITH THE SAME SUM. FROM THE CHOICES ABOVE, ONLY TWO OF THEM ARE POSSIBLE NOW. 1,6,6 - SUM(1,6,6) = 13 2,2,9 - SUM(2,2,9) = 13 WHEN TOM HEARD THAT THE ELDEST IS VISITING HIS GRANDFATHER, WE CAN ELIMINATE COMBINATION 1 SINCE THERE ARE TWO ELDEST ONES. THIS LEAVES US WITH ONLY 1 OPTION LEFT, THAT IS 2, 2 AND 9 IT WILL TAKE 2 HOURS TO MEET. METHOD 1: IGNORE THE SPEED OF THE STREAM, AS THE BOBBER WILL BE CARRIED ALONG AT THREE MILES PER HOUR AS WILL YOU. IT TAKES TWO HOURS TO TRAVEL FOURTEEN MILES, AT A RATE OF SEVEN MILES PER HOUR. METHOD 2: AS THE BOBBER TRAVELS AT 3 MPH, IT WILL BE SIX MILES CLOSER TO YOU IN TWO HOURS. THE DISTANCE BETWEEN YOU AND THE BOBBER BECOMES 8 MILES (14 - 6). IN TWO HOURS YOU WOULD HAVE TRAVELLED 8 ( (7-3) X 2 ) MILES THE TRAIN IS MOVING AT 40 MILES PER HOUR. IMAGINE THAT A FRIEND IS WALKING WITH YOU. WHEN THE TRAIN WHISTLE BLOWS, YOU HEAD AWAY FROM THE TRAIN, HE HEADS TOWARD IT. WHEN HE REACHES SAFETY, YOU WILL BE 6/8 (OR 3/4)OF THE WAY ACROSS THE BRIDGE, AND THE TRAIN WILL HAVE JUST REACHED THE BRIDGE. FOR THE TRAIN TO CROSS 4/4 OF THE BRIDGE IN THE TIME YOU CROSS THE REMAINING 1/4, THE TRAIN MUST BE MOVING FOUR TIMES YOUR SPEED THE PROBABILITY OF THE ANTS COLLIDING IS 0.75. EACH ANT CAN MOVE IN 2 DIFFERENT DIRECTIONS. BECAUSE THERE ARE 3 ANTS, THIS MEANS THAT THERE ARE 23 (8) POSSIBLE WAYS THAT THE ANTS CAN MOVE. NOW, THERE WILL NEVER BE A COLLISION BETWEEN ANY OF THE ANTS IF THEY ARE ALL WALKING IN THE SAME DIRECTION. AND, THE ONLY TIME THEY WILL BE WALKING IN THE SAME DIRECTION IS IF THEY ARE ALL WALKING EITHER CLOCKWISE OR COUNTER-CLOCKWISE AROUND THE TRIANGLE. SO, THERE ARE ONLY TWO SCENARIOS IN WHICH A COLLISION WILL NOT HAPPEN BETWEEN THE ANTS. THIS MEANS THAT THERE ARE 6 SCENARIOS WHERE THE ANTS WILL COLLIDE. AND 6 OUT OF 8 POSSIBLE SCENARIOS, MEANS THAT THE PROBABILITY OF COLLISION IS 6/8, WHICH EQUALS 3/4 OR 0.75. THUS, THE PROBABILITY OF THE ANTS COLLIDING IS 0.75