vanhove@XN.LL.MIT.EDU (Patrick Van Hove) (08/29/87)
I had a somewhat different story of the same type. A door-to-door vacuum cleaner sales person tries his pitch to this uncompassionate mother-at-home-with-kids-screaming-behind and after two minutes, the following dialog ensues mother: Before you go any further, I just want to see if you are really as much >mister-smart< as you pretend. Let's see. My husband noticed a while ago that since the last birthday, the product of the ages of my three daughters is exactly the number on our house. If I add that the sum of their ages is 13, can you figure out how old they are? (Note: integer ages; integer house-numbers;) salesman (after thinking for a while): Well, I think I'm sorry I can't mother: OK, you're right, I made it tough on you, but I have to go now and drive my oldest daughter to her piano lesson. salesman: Your oldest daughter? Well then, I think I know the answer now: their ages are >CENSORED<, >CENSORED< and >CENSORED<. mother: Now I'm impressed! I'll get a dozen of those cleaners of yours. Well, reader, can you figure it out now? Of course you don't even know the number on the house, but who said this was going to be easy? Patrick "No wind today, so I'm hacking"
des@jplpro.JPL.NASA.GOV (David Smyth) (08/31/87)
Nine, and twins of two? The street address is 36.
lewisd@homxc.UUCP (D.LEWIS) (08/31/87)
In article <668@xn.LL.MIT.EDU>, vanhove@XN.LL.MIT.EDU (Patrick Van Hove) writes: > > I had a somewhat different story of the same type. > > mother: Before you go any further, I just want to see if you are really > as much >mister-smart< as you pretend. Let's see. > My husband noticed a while ago that since the last birthday, > the product of the ages of my three daughters is exactly > the number on our house. If I add that the sum of their ages > is 13, can you figure out how old they are? > > (Note: > integer ages; > integer house-numbers;) (edited - mother refers to "oldest daughter") > salesman: > Your oldest daughter? Well then, I think I know the answer now: > their ages are >CENSORED<, >CENSORED< and >CENSORED<. > The key is noticing that there must be only a single answer of the form n,n,n+p for ages. The solution, then is in listing out the possibilities: n n n+p product ================ 1 1 11 11 2 2 9 36 3 3 7 42 4 4 5 80 5 5 3 75 6 6 1 36 So, because the salesman couldn't tell the difference immediately but was able to after he was told that there was a single oldest daughter, we know that the house number is 36 and that the daughters are 2, 2, and 9. -- David B. Lewis {ihnp4!}homxc!lewisd 201-615-5306 Eastern Time, Days.
lewisd@homxc.UUCP (D.LEWIS) (08/31/87)
In article <1064@homxc.UUCP>, lewisd@homxc.UUCP (D.LEWIS) writes: > In article <668@xn.LL.MIT.EDU>, vanhove@XN.LL.MIT.EDU (Patrick Van Hove) writes: > > > > I had a somewhat different story of the same type. > > > > mother: Before you go any further, I just want to see if you are really > > as much >mister-smart< as you pretend. Let's see. > > My husband noticed a while ago that since the last birthday, > > the product of the ages of my three daughters is exactly > > the number on our house. If I add that the sum of their ages > > is 13, can you figure out how old they are? > > > > (Note: > > integer ages; > > integer house-numbers;) > (edited - mother refers to "oldest daughter") > > salesman: > > Your oldest daughter? Well then, I think I know the answer now: > > their ages are >CENSORED<, >CENSORED< and >CENSORED<. > > > I wrote: > The key is noticing that there must be only a single answer of the > form n,n,n+p for ages. The solution, then is in listing out the possibilities: > n n n+p product > ================ > 1 1 11 11 > 2 2 9 36 > 3 3 7 42 > 4 4 5 80 > 5 5 3 75 > 6 6 1 36 > So, because the salesman couldn't tell the difference immediately but was > able to after he was told that there was a single oldest daughter, we > know that the house number is 36 and that the daughters are 2, 2, and 9. Aside from the fact that I can't multiply 3,3,and 7 correctly, I erred in the solution. It is true that the key is in realizing that the salesman can come up with two or more answers -- an answer being x,y,z such that x+y+z=13 and all such pairs have the same product or set of products -- but that when he is told that the oldest daughter is not a twin the answer is unique. It turns out that there are only 14 possibilities. Of these, only two pairs have the same value -- the two mentioned above. And then 2,2,9 is deducible. Sorry for the goof. I'm beating this into the ground. -- David B. Lewis {ihnp4!}homxc!lewisd 201-615-5306 Eastern Time, Days.
marty1@houdi.UUCP (M.BRILLIANT) (09/01/87)
In article <1065@homxc.UUCP>, lewisd@homxc.UUCP (D.LEWIS) writes: > In article <1064@homxc.UUCP>, lewisd@homxc.UUCP (D.LEWIS) writes: > > In article <668@xn.LL.MIT.EDU>, vanhove@XN.LL.MIT.EDU (Patrick Van Hove) writes: > > > the product of the ages of my three daughters is exactly > > > the number on our house. If I add that the sum of their ages > > > is 13, can you figure out how old they are? > > > ..... > > > Your oldest daughter? Well then, I think I know the answer now: > > > their ages are >CENSORED<, >CENSORED< and >CENSORED<. After a false start... > ..... It is true that the key is in realizing > that the salesman can come up with two or more answers ... > ..... but that when he is told that the oldest > daughter is not a twin the answer is unique. > > It turns out that there are only 14 possibilities..... There are only TWO possible answers with twin eldest daughters: (1,6,6) with a product of 36, and (3,5,5) with a product of 75. The house number must be 36 because no other answer is possible for 75. If the product is 36 and the largest factor is unique, the only possible answer is (2,2,9), which is the answer first given by lewisd@homxc.UUCP (D.LEWIS) for the wrong reason. I don't know what this has to do with AI. It's a test of real intelligence. Who else solved it without a scrathpad? M. B. Brilliant Marty AT&T-BL HO 3D-520 (201)-949-1858 Holmdel, NJ 07733 ihnp4!houdi!marty1
colin@pdn.UUCP (09/02/87)
In article <1295@houdi.UUCP>, marty1@houdi.UUCP (M.BRILLIANT) writes: > > ..... It is true that the key is in realizing > > that the salesman can come up with two or more answers ... > > ..... but that when he is told that the oldest > > daughter is not a twin the answer is unique. In the original story, the reference made by the mother to the respective ages of her daughters is: "mother: OK, you're right, I made it tough on you, but I have to go now and drive my oldest daughter to her piano lesson." If the ages of the daughters are 1, 2, and 10, she has an oldest daughter. The various solvers seem to have made the assumption that the other two daughters are the same age. > I don't know what this has to do with AI. It's a test of real > intelligence. Who else solved it without a scrathpad? I did, by refraining from making an unwarranted assumption. -- Colin Kendall Paradyne Corporation {gatech,akgua}!usfvax2!pdn!colin Mail stop LF-207 Phone: (813) 530-8697 8550 Ulmerton Road, PO Box 2826 Largo, FL 33294-2826
marty1@houdi.UUCP (M.BRILLIANT) (09/03/87)
In article <1238@pdn.UUCP>, colin@pdn.UUCP (Colin Kendall) writes: > In article <1295@houdi.UUCP>, marty1@houdi.UUCP (M.BRILLIANT) writes: > > > ..... It is true that the key is in realizing > > > that the salesman can come up with two or more answers ... > > > ..... but that when he is told that the oldest > > > daughter is not a twin the answer is unique. > > In the original story, the reference made by the mother > to the respective ages of her daughters is: > > "mother: OK, you're right, I made it tough on you, but I have to go > now and drive my oldest daughter to her piano lesson." > > If the ages of the daughters are 1, 2, and 10, she has an oldest > daughter. The various solvers seem to have made the > assumption that the other two daughters are the same age. Only one solver made that incorrect assumption, in his first posting. Instead, our key clue is that the salesman needed the clue that there was an oldest daughter, and not two oldest daughters the same age. Your proposed solution is too easy, because then the salesman would not have needed that clue. The house number (product of the ages) would be 20, which can be uniquely decomposed into three factors whose sum is 13. > > I don't know what this has to do with AI. It's a test of real > > intelligence. Who else solved it without a scrathpad? > > I did, by refraining from making an unwarranted assumption. Nice try, but no cigar. I still don't know what this has to do with AI (pardon my misspelling of scratchpad). M. B. Brilliant Marty AT&T-BL HO 3D-520 (201)-949-1858 Holmdel, NJ 07733 ihnp4!houdi!marty1
lewisd@homxc.UUCP (D.LEWIS) (09/03/87)
In article <1238@pdn.UUCP>, colin@pdn.UUCP (Colin Kendall) writes: > In article <1295@houdi.UUCP>, marty1@houdi.UUCP (M.BRILLIANT) writes: > > > ..... It is true that the key is in realizing > > > that the salesman can come up with two or more answers ... > > > ..... but that when he is told that the oldest > > > daughter is not a twin the answer is unique. > > In the original story, the reference made by the mother > to the respective ages of her daughters is: > > "mother: OK, you're right, I made it tough on you, but I have to go > now and drive my oldest daughter to her piano lesson." > > If the ages of the daughters are 1, 2, and 10, she has an oldest > daughter. The various solvers seem to have made the > assumption that the other two daughters are the same age. > > > I don't know what this has to do with AI. It's a test of real > > intelligence. Who else solved it without a scrathpad? > > I did, by refraining from making an unwarranted assumption. So the house number is 20, and the solution is unique. Why didn't the salesman reply immediately? He missed the quick kill because the information was insufficient at first. Only after the quote above did he have enough info. PS: There is also a unique solution with the sum of the ages equal to 14, I believe. -- David B. Lewis {ihnp4!}homxc!lewisd 201-615-5306 Eastern Time, Days.
thorp@mmlai.UUCP (John Thorp) (09/04/87)
Before this gets out of hand... It seems the trick to seeing the solution is to realize the YOU are a third party to the dialog. Just because the author has choosen not to give the house number in the problem DOES NOT mean the saleaman does not know the house number. For a matter of fact, the salesman can observe the house number. His response of "no I can not tell you the age of your daughters" leeds us to one of two conclusions: 1) the solution is not unique for the house number he is observing. [.ie (1,6,6) (2,2,9)] NOTE: The only house number to produce more than one solution is 36, so this must be the house. or 2) He is incapable of solving the problem for the given house number. [.ie "I can't solve this problem!"] We all know that salesmen will do anything for a sale, even correctly solve math problems :-), so option 2 can not be the case. If the house number had provided a unique solution [ie. (1,2,10)], then the salesman would have responded with the proper triple and been done with it. If you follow the above, then the final paragraph by the housewife selects which of the TWO possible solutions is the correct one. (there exists an oldest daughter, singular) -> (2,2,9) Remember: The key is you, the reader, are an observer not a participant. > In article <1238@pdn.UUCP>, colin@pdn.UUCP (Colin Kendall) writes: > > In article <1295@houdi.UUCP>, marty1@houdi.UUCP (M.BRILLIANT) writes: > > > > "mother: OK, you're right, I made it tough on you, but I have to go > > now and drive my oldest daughter to her piano lesson." > > > > If the ages of the daughters are 1, 2, and 10, she has an oldest > > daughter. The various solvers seem to have made the > > assumption that the other two daughters are the same age. > | Its not up to YOU to choose a house number the | salesman can see it himself. VV > So the house number is 20, and the solution is > unique. Why didn't the salesman reply > immediately? He missed the quick kill because the information > was insufficient at first. Only after the quote above did he have > enough info. HE had enough info all along. If he had responded with (1,2,10) The housewife would have looked at him, looked at the number (36) and slammed the door. I hope this helped ! comp.ai maybe... rec.puzzles yes! -- John Thorp @ Martin Marietta Labs / Artificial Intelligence Department ARPA: thorp@mmlai.uu.net UUCP: {uunet, super, hopkins!jhunix} !mmlai!thorp
colin@pdn.UUCP (Colin Kendall) (09/04/87)
In article <1303@houdi.UUCP#, marty1@houdi.UUCP (M.BRILLIANT) writes: # In article <1238@pdn.UUCP>, colin@pdn.UUCP (Colin Kendall) writes: # > If the ages of the daughters are 1, 2, and 10, she has an oldest # > daughter. The various solvers seem to have made the # > assumption that the other two daughters are the same age. # # Only one solver made that incorrect assumption, in his first posting. Agreed. # Instead, our key clue is that the salesman needed the clue that there # was an oldest daughter, and not two oldest daughters the same age. # # Your proposed solution is too easy, because then the salesman would not # have needed that clue. The house number (product of the ages) would be # 20, which can be uniquely decomposed into three factors whose sum is 13. 1,2,10 was not a proposed solution, just an example. I intended to convey that the solution was impossible. After reviewing all the related postings more carefully, I see. The faulty assumption that *all* the solvers made was that the salesman knew the house number. I didn't make that one. -- Colin Kendall Paradyne Corporation {gatech,akgua}!usfvax2!pdn!colin Mail stop LF-207 Phone: (813) 530-8697 8550 Ulmerton Road, PO Box 2826 Largo, FL 33294-2826
merlyn@starfire.UUCP (Brian Westley) (09/06/87)
(crossposted to rec.puzzles, followups there please) Given: ages A,B, and C, such that A+B+C=13 and A*B*C equals some number; the solution is ambiguous until you are told that one number is largest (i.e. this eliminates an answer where there are two equal larger numbers). Answer: A=9, B=2, C=2; A*B*C = 36. The ambiguous case is A=6, B=6, C=1 Merlyn Leroy
alan@pdn.UUCP (09/12/87)
In article <1238@pdn.UUCP> colin@pdn.UUCP (Colin Kendall) writes:
/In the original story, the reference made by the mother
/to the respective ages of her daughters is:
/ "mother: OK, you're right, I made it tough on you, but I have to go
/ now and drive my oldest daughter to her piano lesson."
/If the ages of the daughters are 1, 2, and 10, she has an oldest
/daughter. The various solvers seem to have made the
/assumption that the other two daughters are the same age.
/> I don't know what this has to do with AI. It's a test of real
/> intelligence. Who else solved it without a scrathpad?
/I did, by refraining from making an unwarranted assumption.
Hi Colin.
Are you saying the answer is 1, 2 and 10 because that means there is an
oldest daughter? Then why not pick 13, 0, 0 or 7, 4, 2 (or whatever)?
Or did you mean that the reasoning of the other "solvers" is faulty
because there could be two daughters, both age "six", one ten months
"older" than the other?
--alan@pdn