T H _
C H _ L D R _ N
_ R _
1 ,
6
_ N D
6
Y _ _ R S
_ L D .
T H _
P R _ D _ C T
_ F
T H _ _ R
_ G _ S
_ S
3 6 ,
S _
N _ N _
_ F
T H _ M
C _ N
B _
_ L D _ R
T H _ N
3 6 .
T H _
N _ M B _ R
3 6
H _ S
T _
B _
_ X P R _ S S _ D
_ S
T H _
P R _ D _ C T
_ F
3
N _ M B _ R S .
T H _ _ R
P _ S S _ B L _
_ G _ S
_ R _
( T H _
S _ M
_ F
T H _ _ R
_ G _ S
_ S
_ N
B R _ C K _ T S ) :
1 ,
1 ,
3 6
( 3 9 3 8 )
1 ,
2 ,
1 8
( 2 1 )
1 ,
3 ,
1 2
( 1 6 )
1 ,
4 ,
9
( 1 4 )
1 ,
6 ,
6
( 1 3 )
2 ,
2 ,
9
( 1 3 )
2 ,
3 ,
6
( 1 1 )
3 ,
3 ,
4
( 1 0 )
S _ N C _
C H _ R Y L
_ S
T _ M ' S
N _ X T
D _ _ R
N _ _ G H B _ _ R ,
T _ M
K N _ W S
C H _ R Y L ' S
H _ _ S _
N _ M B _ R .
T _ M
W _ _ L D
K N _ W
T H _
C H _ L D R _ N ' S
_ G _ S
_ N
_ V _ R Y
C _ S _
T H _ T
S _ M S
_ P
T _
_
_ N _ Q _ _
N _ M B _ R
_ X C _ P T
F _ R
T H _
S _ M
_ F
1 3 ,
W H _ C H
H _ V _
2
C _ M B _ N _ T _ _ N S
_ F
P _ S S _ B L _
_ G _ S .
A S
_
R _ S _ L T ,
T _ M
W _ _ L D
B _
C _ N F _ S _ D
_ S
H _
H _ S
T _
P _ C K
B _ T W _ _ N
T H _
2
C _ M B _ N _ T _ _ N S :
( 1 , 6 , 6 )
_ N D
( 2 , 2 , 9 ) .
C H _ R Y L
T H _ N
T _ L L S
T _ M
_ B _ _ T
H _ R
Y _ _ N G _ S T
C H _ L D
W H _
L _ K _ S
S T R _ W B _ R R Y
M _ L K
W H _ C H
T _ L L S
T _ M
T H _ T
T H _ R _
_ S
_ N L Y
1
Y _ _ N G _ S T
C H _ L D Clue
WHEN THE FIRST SERVANT COMES IN, THE KING SHOULD WRITE DOWN HIS NUMBER. FOR EACH OTHER SERVANT THAT REPORTS IN, THE KING SHOULD ADD THAT SERVANT'S NUMBER TO THE CURRENT NUMBER WRITTEN ON THE PAPER, AND THEN WRITE THIS NEW NUMBER ON THE PAPER. LET X BE THE NUMBER OF THE MISSING SERVANT AND Y BE THE NUMBER THAT THE KING HAS WRITTEN. ONCE THE FINAL SERVANT HAS REPORTED IN, THE NUMBER ON THE PAPER SHOULD EQUAL: Y = (1 + 2 + 3 + ... + 99 + 100) - X (1 + 2 + 3 + ... + 99 + 100) = 5050, SO WE CAN REPHRASE THIS TO SAY THAT THE NUMBER ON THE PAPER SHOULD EQUAL: Y = 5050 - X SO TO FIGURE OUT THE MISSING SERVANT'S NUMBER, THE KING SIMPLY NEEDS TO SUBTRACT THE NUMBER WRITTEN ON HIS PAPER FROM 5050: 5050 - Y = X THE CHILDREN ARE 1, 6 AND 6 YEARS OLD. THE PRODUCT OF THEIR AGES IS 36, SO NONE OF THEM CAN BE OLDER THAN 36. THE NUMBER 36 HAS TO BE EXPRESSED AS THE PRODUCT OF 3 NUMBERS. THEIR POSSIBLE AGES ARE (THE SUM OF THEIR AGES IS IN BRACKETS): 1, 1, 36 (3938) 1, 2, 18 (21) 1, 3, 12 (16) 1, 4, 9 (14) 1, 6, 6 (13) 2, 2, 9 (13) 2, 3, 6 (11) 3, 3, 4 (10) SINCE CHERYL IS TOM'S NEXT DOOR NEIGHBOUR, TOM KNOWS CHERYL'S HOUSE NUMBER. TOM WOULD KNOW THE CHILDREN'S AGES IN EVERY CASE THAT SUMS UP TO A UNIQUE NUMBER EXCEPT FOR THE SUM OF 13, WHICH HAVE 2 COMBINATIONS OF POSSIBLE AGES. AS A RESULT, TOM WOULD BE CONFUSED AS HE HAS TO PICK BETWEEN THE 2 COMBINATIONS: (1,6,6) AND (2,2,9). CHERYL THEN TELLS TOM ABOUT HER YOUNGEST CHILD WHO LIKES STRAWBERRY MILK WHICH TELLS TOM THAT THERE IS ONLY 1 YOUNGEST CHILD THE ELDEST IS 8 YEARS OLD AND THE 2 YOUNGER ONES ARE 3 YEARS OLD. LET'S BREAK IT DOWN. THE PRODUCT OF THEIR AGES IS 72. SO THE POSSIBLE CHOICES ARE: 2, 2, 18 - SUM(2, 2, 18) = 22 2, 4, 9 - SUM(2, 4, 9) = 15 2, 6, 6 - SUM(2, 6, 6) = 14 2, 3, 12 - SUM(2, 3, 12) = 17 3, 4, 6 - SUM(3, 4, 6) = 13 3, 3, 8 - SUM(3, 3, 8 ) = 14 1, 8, 9 - SUM(1,8,9) = 18 1, 3, 24 - SUM(1, 3, 24) = 28 1, 4, 18 - SUM(1, 4, 18) = 23 1, 2, 36 - SUM(1, 2, 36) = 39 1, 6, 12 - SUM(1, 6, 12) = 19 THE SUM OF THEIR AGES IS THE SAME AS YOUR BIRTH DATE. THAT COULD BE ANYTHING FROM 1 TO 31 BUT THE FACT THAT JACK WAS UNABLE TO FIND OUT THE AGES, IT MEANS THERE ARE TWO OR MORE COMBINATIONS WITH THE SAME SUM. FROM THE CHOICES ABOVE, ONLY TWO OF THEM ARE POSSIBLE NOW. 2, 6, 6 - SUM(2, 6, 6) = 14 3, 3, 8 - SUM(3, 3, 8 ) = 14 SINCE THE ELDEST KID IS TAKING PIANO LESSONS, WE CAN ELIMINATE COMBINATION 1 SINCE THERE ARE TWO ELDEST ONES. THE ANSWER IS 3, 3 AND 8 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