I was chatting with an older friend of mine when I happened to mention the ages of my two children. He said to me, "when your youngest was born your age was the square of the older one. Now your age is the product of both their ages."

I then thought about his age and the ages of his children and replied, "When your youngest was born your age was the product of the older two. Later on your age was the product of the oldest and youngest. Now your age is the product of the younger two."

What are our two ages?

(Assume we all have the same birthday.)

DEFDBL A-Z
CLS
PRINT "narrator:"
FOR father = 15 TO 70
 FOR d1 = 2 TO father - 13
  FOR d2 = 1 TO d1 - 1
    t1father = father - d2
    t1oldest = d1 - d2
    IF t1father = t1oldest * t1oldest THEN
      IF father = d1 * d2 THEN PRINT father, d1, d2
    END IF
  NEXT
 NEXT
NEXT

PRINT : PRINT "friend:"
FOR father = 15 TO 70
 FOR d1 = 3 TO father - 13
  FOR d2 = 2 TO d1 - 1
    FOR d3 = 1 TO d2 - 1
      t1father = father - d3
      t1oldest = d1 - d3
      t1middle = d2 - d3
      IF t1father = t1oldest * t1middle THEN
        good = 0
        FOR yago = d3 - 1 TO 1 STEP -1
          t1father = father - yago
          t1oldest = d1 - yago
          t1middle = d2 - yago
          t1youngest = d3 - yago
          IF t1father = t1oldest * t1youngest THEN good = 1: EXIT FOR
        NEXT yago
        IF good THEN IF father = d2 * d3 THEN PRINT father, d1, d2, d3, yago
      END IF
    NEXT
  NEXT
 NEXT
NEXT

finds

narrator:
 40            10            4

friend:
 66            18            11            6             2

so the narrator is 40 and his friend is 66.

The narrator's children are 10 and 4; the friend's children are 18, 11 and 6, and the "later on" in the narrator's description of the friend's situation was 2 years ago, when the friend was 64, the product of 16 and 4.

Posted by Charlie on 2013-01-22 16:48:29