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Some Sum Squares To Product (Posted on 2008-11-22) Difficulty: 2 of 5
The product of the ages of Timothy’s children is the square of the sum of their ages. Timothy has at least 2 children but less than 8 children. All of his children are at least 2 years old and at most 14 years old. All the ages of the children are different and the age of each child is a positive integer when expressed in years.

How many children are there and what are their ages?

See The Solution Submitted by K Sengupta    
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Solution computer solution Comment 1 of 1
DECLARE SUB choose (child!)
DIM SHARED n, childage(8)
CLS

FOR n = 2 TO 7
  choose 1
NEXT

SUB choose (child)
  st = 2
  IF child > 1 THEN
    st = childage(child - 1) + 1
  END IF
  FOR age = st TO 14
     childage(child) = age
     IF child < n THEN
      choose child + 1
     ELSE
      prod = 1: sum = 0
      FOR i = 1 TO n
        prod = prod * childage(i)
        sum = sum + childage(i)
      NEXT i
      IF prod = sum * sum THEN
        FOR i = 1 TO n
          PRINT childage(i);
        NEXT i
        PRINT , prod; sum: PRINT
      END IF
     END IF
  NEXT age
END SUB

produces

2  4  6  12   576  24

indicating four children, ages 2, 4, 6 and 12, adding to 24 and multiplying out to 576.

  Posted by Charlie on 2008-11-22 19:57:52
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