postpischil@being.DEC (Always mount a scratch monkey.) (01/30/86)
decwrl!amdcad!lll-crg!mordor!ut-sally!bulko (Bill Bulko) writes: > wasaunders@watdragon.UUCP (Alec Saunders) writes: > . . . > > "The sum of their ages is thirteen, the product of their ages > > is as old as you are. The oldest weighs 61 pounds." > . . . > The weight of the oldest child is probably meant to be used as a constraint > for his age. However, I think the information given is inadequate for a > solution unless we make a few (reasonable) assumptions: (1) that the children > are at least one year apart from each other in age (since there was no mention > of twins); (2) that the man's age is appropriate for the age of his children; > and (3) the friend's age is roughly equal to that of the man (a *major* > assumption). Actually, I believe the purpose of stating the weight is different. The deductions we are supposed to make probably are: 1) The friend was able to determine the ages from the information given. 2) That determination could not have been made if the statement about the weight of the oldest child were absent. 3) The reference to an "oldest child" was intended to tell us that there was an oldest child instead of two equally old twins -- an imprecise statement since even twins are rarely born at exactly the same time. Given the second deduction, we know that the friend was unable to determine the ages of the children even knowing the product of their ages (since we may presume the friend's age was known to the friend). Of the possible selections of three positive integers that add up to 13, only two selections have the same product, 36. Each of the other possible selections has a unique product, and this would make it possible for the friend to have identified the selection. The two selections are 2, 2, and 9 and 1, 6, and 6. Since the latter case is ruled out by the third deduction, the ages are 2, 2, and 9. I would also like to point out that another assumption that Bill Bulko should not have made is that the parent is male. -- edp (Eric Postpischil) "Always mount a scratch monkey."