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All in the family (Posted on 2011-11-20) Difficulty: 2 of 5
Teenager A: I found an interesting relation between my age and the age of my father. Multiplying my age by the age of my father I get the same result if we use the correct ages or if both of us reverse the ages' digits prior to the multiplication.
Same happens if I do it with my grandfather's or even with my aged grand-grand father's ages.
B, A's brother: That applies to my age as well.
C, a friend: My age, too. But no grand-grandfather...
All the ages (A,B,C) are distinct.
What are they?

No Solution Yet Submitted by Ady TZIDON    
Rating: 4.5000 (2 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts computer exploration--I'm only getting two | Comment 1 of 17

I assume that a teenager is somewhere between 13 and 19 inclusive, and that generations are between 12 and 77 years apart:

CLS
FOR teen = 13 TO 19
 revteen = (teen MOD 10) * 10 + (teen \ 10)
 FOR father = teen + 12 TO teen + 77
   revfath = (father MOD 10) * 10 + (father \ 10)
   IF teen * father = revteen * revfath THEN
     FOR grand = father + 12 TO father + 77
       grands$ = LTRIM$(STR$(grand))
       r$ = ""
       FOR i = 1 TO LEN(grands$)
        r$ = MID$(grands$, i, 1) + r$
       NEXT
       revgrand = VAL(r$)
       IF teen * grand = revteen * revgrand THEN
           PRINT teen, father, grand
           FOR great = grand + 12 TO grand + 77
               greats$ = LTRIM$(STR$(great))
               r$ = ""
               FOR i = 1 TO LEN(greats$)
                r$ = MID$(greats$, i, 1) + r$
               NEXT
               revgreat = VAL(r$)
               IF teen * great = revteen * revgreat THEN
                 PRINT teen, father, grand, great
               END IF
           NEXT
       END IF
     NEXT grand
   END IF
 NEXT father
NEXT teen

but it still finds only the following possibilities for the teenagers' ages and preceding generations, even allowing for 3-digit ages:

 13            31            62
 13            31            62            93
 13            31            93
 13            62            93
 14            41            82
 


 What's immediately striking is there are only two possible teen ages, thought he puzzle calls for three. The best I can come up with is that C is 14, with father and grandfather at 41 and 82 respectively, while A's (or is it B's) age is 13, with the generations going backward as 31, 62 and 93.


  Posted by Charlie on 2011-11-20 16:49:13
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