A man and his grandson have the same birthday. For six consecutive years, the man's age was a exact multiple of the boy's age. How old were they at the last birthday?

The biblical patriarchs, it is written, lived as old as 969 years (Methuselah) and fathered children as old as 500 years (Noah). Accepting this, it is conceivable that one could have been 420 years old at the birth of one's grandchild and have an age that was a multiple of the grandchild's age for the next 7 years, or even to have been 840 years old, and have an age that was a multiple of the grandchild's for the next 8 years.

grandson grandfather
    1             421       = (421 * 1)
    2             422       = (211 * 2)
    3             423       = (141 * 3)
    4             424       = (106 * 4)
    5             425       = ( 85 * 5)
    6             426       = ( 71 * 6)
    7             427       = ( 61 * 7)

    1             841       = (841 * 1)
    2             842       = (421 * 2)
    3             843       = (281 * 3)
    4             844       = (211 * 4)
    5             845       = (169 * 5)
    6             846       = (141 * 6)
    7             847       = (121 * 7)
    8             848       = (106 * 8)

Posted by Dej Mar on 2011-04-18 06:42:22