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
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 HE IS 16 YEARS OLD. WHEN I WAS 4 YEARS OLD, MY BROTHER WAS 2 YEARS OLD (HALF MY AGE), SO MY BROTHER IS 2 YEARS YOUNGER THAN ME. WHEN I AM 18 YEARS OLD, MY BROTHER WILL BE 16 YEARS OLD AS HE IS 2 YEARS YOUNGER THAN ME CHERYL'S BIRTHDAY IS ON JULY 16. FROM ALBERT'S FIRST STATEMENT, WE CAN ELIMINATE MAY AND JUNE. THE DATES MAY 19 AND JUNE 18 ARE UNIQUE (19 ONLY APPEARS IN MAY 19 AND 18 ONLY APPEARS IN JUNE 18) AND IF THERE IS NO WAY FOR BERNARD TO KNOW CHERYL'S BIRTHDAY, THEN IT CANNOT BE MAY OR JUNE. BERNARD CAN NOW ELIMINATE MAY AND JUNE AFTER ALBERT'S FIRST STATEMENT. IF BERNARD CAN NOW DEDUCE CHERYL'S BIRTHDAY, THE DATE HAS TO BE UNIQUE. THEREFORE, WE CAN ELIMINATE JULY 14 AND AUG 14 AS WELL. NOW WE ARE LEFT WITH JULY 16, AUG 15 OR AUG 17. ALBERT NOW KNOWS IT CAN ONLY BE JULY 16, AUG 15 OR AUG 17. HE KNOWS THE MONTH BUT NOT THE DATE, AND THAT IS ENOUGH TO TELL HIM THE CORRECT ANSWER. THEREFORE IT CAN ONLY BE JULY 16. IF IT HAD BEEN AUGUST, THEN HE WILL NOT KNOW IF IT IS AUG 15 OR AUG 17 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)