ins_akaa@jhunix.UUCP (Ken Arromdee) (01/29/86)
>This is a puzzle which someone told me the other day. I have no solution as >yet - perhaps some of you creative types can come up with one. > Two friends are walking down the street. One says to the other "Do > you have any children?". The other replies "Yes - three sons". > The first asks "How old are they?", to which the second replies > "The sum of their ages is thirteen, the product of their ages > is as old as you are. The oldest weighs 61 pounds." > How old are the three sons? For that matter how old is the friend? > And what does the eldest weight have to do with anything??? First, you stated the problem incorrectly. You left out the statement by the friend that the sum and product aren't sufficient information, but that the friend could then solve the problem after being told "The eldest weighs 61 pounds". There are several possibilities: 1,1,11; 1,2,10; 1,3,9; 1,4,8; 1,5,7; 1,4,6; 2,2,9; 2,3,8; 2,4,7; 2,5,6; 3,3,7; 3,4,6. The eldest weight has nothing to do with weight, but can be used to infer that there is an "eldest"--the possibilities 1,6,6; 3,5,5 aren't good. Now, the respective products are 11; 20; 27; 32; 35; 24; 36; 48; 56; 60; 63; 72. In most of these cases there is a unique product, and thus the friend doesn't need the additional information that there exists an oldest son. However, the case 2,2,9 has the same product (36) as the case 1,6,6. Only in this case, friend's age=36, is the friend unable to solve the problem until told there is an oldest child. Therefore the friend's age is 36 and the childrens' ages are 2,2,9. -- "We are going to give a little something, a few little years more, to socialism, because socialism is defunct. It dies all by iself. The bad thing is that socialism, being a victim of its... Did I say socialism?" -Fidel Castro Kenneth Arromdee BITNET: G46I4701 at JHUVM and INS_AKAA at JHUVMS CSNET: ins_akaa@jhunix.CSNET ARPA: ins_akaa%jhunix@hopkins.ARPA UUCP: ...allegra!hopkins!jhunix!ins_akaa