G R _ N D F _ T H _ R
W _ S
6 6
_ N D
G R _ N D S _ N
W _ S
6 .
W H _ N
G R _ N D F _ T H _ R
W _ S
6 1 ,
G R _ N S _ N
W _ S
1
( 6 1
=
1
X
6 1 )
W H _ N
G R _ N D F _ T H _ R
W _ S
6 2 ,
G R _ N S _ N
W _ S
2
( 6 2
=
2
X
3 1 )
W H _ N
G R _ N D F _ T H _ R
W _ S
6 3 ,
G R _ N S _ N
W _ S
3
( 6 3
=
3
X
2 1 )
W H _ N
G R _ N D F _ T H _ R
W _ S
6 4 ,
G R _ N S _ N
W _ S
4
( 6 4
=
4
X
1 6 )
W H _ N
G R _ N D F _ T H _ R
W _ S
6 5 ,
G R _ N S _ N
W _ S
5
( 6 5
=
5
X
1 3 )
W H _ N
G R _ N D F _ T H _ R
W _ S
6 6 ,
G R _ N S _ N
W _ S
6
( 6 6
=
6
X
1 1 ) Clue
SHE IS 25 YEARS OLD. IF 2 AND 5 CHANGE PLACES, YOU WILL GET 52. SHE WILL TURN 26 NEXT YEAR, AND IF YOU DOUBLE THAT NUMBER, YOU WILL GET 52 18 YEARS OLD. LET MY AGE BE X YEARS NOW. MY AGE AFTER 3 YEARS IS (X+3). MY AGE 3 YEARS AGO IS (X-3). SO, NOW WE CAN COME UP WITH AN EQUATION FOR X: X=3(X+3)-3(X-3) SOLVING FOR X WILL GIVE 18 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 GRANDFATHER WAS 66 AND GRANDSON WAS 6. WHEN GRANDFATHER WAS 61, GRANSON WAS 1 (61 = 1 X 61) WHEN GRANDFATHER WAS 62, GRANSON WAS 2 (62 = 2 X 31) WHEN GRANDFATHER WAS 63, GRANSON WAS 3 (63 = 3 X 21) WHEN GRANDFATHER WAS 64, GRANSON WAS 4 (64 = 4 X 16) WHEN GRANDFATHER WAS 65, GRANSON WAS 5 (65 = 5 X 13) WHEN GRANDFATHER WAS 66, GRANSON WAS 6 (66 = 6 X 11)