perplexus.info :: Just Math : Some Sum Squares To Product

Some Sum Squares To Product (Posted on 2008-11-22)

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

Rating: 5.0000 (1 votes)

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computer solution

Comment 1 of 1

DECLARE SUB choose (child!)

DIM SHARED n, childage(8)

CLS

FOR n = 2 TO 7

choose 1

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

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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