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?
I assume that a teenager is somewhere between 13 and 19 inclusive, and that generations are between 12 and 77 years apart:
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$
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$
revgreat = VAL(r$)
IF teen * great = revteen * revgreat THEN
PRINT teen, father, grand, great
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