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T W _
W _ D _ W S
H _ D
_ _ C H
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S _ N ,
_ N D
_ _ C H
W _ D _ W
M _ R R _ _ D
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S _ N
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D _ _ G H T _ R
B Y
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M _ R R _ _ G _ ,
_ L L
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W _ L L
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L _ T ' S
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S 1 .
T H _
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W _ D _ W ,
W 2
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S 2 .
W 1
M _ R R _ _ S
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_ N D
H _ V _
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W 2
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S _
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2
G R _ N D M _ T H _ R S
( W 1 ,
W 2 )
W _ T H
T H _ _ R
2
G R _ N D D _ _ G H T _ R S
( D 2 ,
D 1 )
2
H _ S B _ N D S
( S 1 ,
S 2 )
W _ T H
T H _ _ R
2
W _ V _ S
( W 2 ,
W 1 )
2
F _ T H _ R S
( S 1 ,
S 2 )
W _ T H
T H _ _ R
2
D _ _ G H T _ R S
( D 2 ,
D 1 )
2
M _ T H _ R S
( W 1 , W 2 )
W _ T H
T H _ _ R
2
S _ N S
( S 1 , S 2 )
2
M _ _ D _ N S
( D 1 , D 2 )
W _ T H
T H _ _ R
2
M _ T H _ R S
( W 1 , W 2 )
2
S _ S T _ R S
( D 1 , D 2 )
W _ T H
T H _ _ R
2
( H _ L F )
B R _ T H _ R S
( S 1 , S 2 ) Clue
THE MOTHER WAS THE MURDERER. WE KNOW FROM (3) THAT THE YOUNGEST PERSON WAS NOT THE VICTIM, FROM (4) THAT THE YOUNGEST PERSON WAS NOT THE HELPER AND FROM (6) THAT THE YOUNGEST PERSON WAS NOT THE KILLER. THE YOUNGEST PERSON CAN ONLY HAVE BEEN THE WITNESS THEREFORE. WE CAN WORK OUT FROM (5) THAT THE FATHER WAS THE OLDEST, FROM (2) THAT THE YOUNGEST PERSON MUST HAVE BEEN THE DAUGHTER. THEREFORE THE NEXT TO THE YOUNGEST MUST HAVE BEEN THE SON AND THE NEXT TO THE OLDEST, THE MOTHER. FROM THE STATEMENTS, WE CAN SORT OUT THE MEMBERS BASED ON AGE, FROM OLDEST TO YOUNGEST AS: FATHER, MOTHER, SON, DAUGHTER. WE CAN COME TO THE FOLLOWING CONCLUSION: MOTHER - MURDERER FATHER - HELPER SON - VICTIM DAUGHTER - WITNESS IF THE GIRLS HAD BEEN ON A STANDING TRAIN, THE FIRST GIRL'S CALCULATIONS WOULD HAVE BEEN CORRECT, BUT THEIR TRAIN WAS MOVING. IT TOOK 5 MINUTES TO MEET A SECOND TRAIN, BUT THEN IT TOOK THE SECOND TRAIN 5 MORE MINUTES TO REACH WHERE THE GIRLS MET THE FIRST TRAIN. SO THE TIME BETWEEN TRAINS IS 10 MINUTES, NOT 5, AND ONLY 6 TRAINS PER HOUR ARRIVE IN THE CITY LET: DAD = F (1) MOM = M (2) SON = S (4) DAUGHTER = D (5) THIS IS HOW THEY CROSS THE TUNNEL: F,M → (2) ← F (1) S,D → (5) ← M (2) F,M → (2) THE TIME IN BRACKETS () INDICATE THE TIME TAKEN TO CROSS THE TUNNEL. IF YOU SUM THEM UP, IT WILL ADD UP TO 12 MINUTES IF TWO WIDOWS HAD EACH A SON, AND EACH WIDOW MARRIED THE SON OF THE OTHER AND HAD A DAUGHTER BY THE MARRIAGE, ALL THE RELATIONSHIPS WILL BE FOUND TO RESULT. LET'S SAY THE FIRST WIDOW, W1, HAS A SON, S1. THE SECOND WIDOW, W2 HAS A SON, S2. W1 MARRIES S2 AND HAVE A DAUGHTER D1. W2 MARRIES S1 AND HAVE A DAUGHTER D2. SO WE HAVE: 2 GRANDMOTHERS (W1, W2) WITH THEIR 2 GRANDDAUGHTERS (D2, D1) 2 HUSBANDS (S1, S2) WITH THEIR 2 WIVES (W2, W1) 2 FATHERS (S1, S2) WITH THEIR 2 DAUGHTERS (D2, D1) 2 MOTHERS (W1,W2) WITH THEIR 2 SONS (S1,S2) 2 MAIDENS (D1,D2) WITH THEIR 2 MOTHERS (W1,W2) 2 SISTERS (D1,D2) WITH THEIR 2 (HALF) BROTHERS (S1,S2)