Puzzle of the Month: Popular Science, April 1960

[dvtimes]

Puzzle of the Month: Popular Science, April 1960

[wankmaster]

15,5,3

[WordsforHire]

so i take it we have to guess their ages?

[smoothballs]

he has a crease in only one trouser leg! lol

[Jel]

Is it just me, or is the way he is pressing the doorbell look a bit :gaylords:

[redwhiteandblue]

15,5,3

Why can't it be 1, 9 and 25?

[wankmaster]

Why can't it be 1, 9 and 25?
Good point.

[dvtimes]

I think you also need to say what the house no is too.

[ApacheAnderson]

3, 3, 25 the house number is 31

[redwhiteandblue]

I think he actually knocked on the door of a mental hospital and the person answering was just giving him random replies because he was a fruitcake.

[ApacheAnderson]

I have to confess I googled the answer, but if anyone can work out why is the answer I'd be amazed.

[eman]

25, 3 and 3

[wankmaster]

My answer can't be right 15,5,3 cos that would be 3 kids and the social would have been on to them.

So that would leave 25,3,3 or 25,9,1 now the 1 year old would not have answered the door, so the person who did must have been 25 or 9 or 3. I don't think the 3 year old would have answered the door either, or if he/she did the census man would ask if his mum was in. So we're left with the 25 year old answering the door. So that doesn't solve it does it?

I don't know then.

And also 75, 3 and 1 would also work just as well, as the parents could have been killed in a plane crash and the grandma be looking after the kids.

[eman]

The way I'm looking at it is this ....

Two of the three must be the same age, otherwise there would be no point in determining the hierarchical status of the person who answered the door ..

[ApacheAnderson]

My answer can't be right 15,5,3 cos that would be 3 kids and the social would have been on to them.

So that would leave 25,3,3 or 25,9,1 now the 1 year old would not have answered the door, so the person who did must have been 25 or 9 or 3. I don't think the 3 year old would have answered the door either, or if he/she did the census man would ask if his mum was in. So we're left with the 25 year old answering the door. So that doesn't solve it does it?

I don't know then.

And also 75, 3 and 1 would also work just as well, as the parents could have been killed in a plane crash and the grandma be looking after the kids.

The answer is actually 3, 3, 25. But your not quite there with the working out.

[eman]

And factorisation covers the rest - I think!!

[wankmaster]

The way I'm looking at it is this ....

Two of the three must be the same age, otherwise there would be no point in determining the hierarchical status of the person who answered the door ..

So the 3 year old answered the door? But the 3 year old would not be clever enough with maths, unless he'd been put up to it my his mum.

[wankmaster]

Also one of the twins could not have been the "eldest", so he could not have been taking to either of the 3 year olds. If he had been talking to a twin he would have asked who was the "elder". Maybe.

I dunno.

[eman]

He was talking to the oldest - there are only so many ways to factorise 225.

I think!

[dvtimes]

The ages are 3, 3, and 25. They live in house number 31.


225 has a prime factorization of 1*3*3*5*5. You could have the
following possible age combinations in three people. (1,1,225),
(1,15,15), (3,3,25), (3,15,5), and (9,5,5).

Ages House Number
======== ============
1 1 225 227
3 3 25 31
1 15 15 31
3 15 5 23
9 5 5 19

The census taker knows the house number. Since the census taker must
ask a clarifying question we know that the family does not live at
street number 19, 23, or 227. That leaves 31.

Ages House Number
======== ============
3 3 25 31
1 15 15 31

The census taker asks which if the respondent is the eldest. Since
the answer is yes we know that the respondent is 25, that being the
only remaining group that has an eldest. If it were the other group
the respondent would have said that they were not the eldest and there
is another of the same age.

Ages House Number
======== ============
3 3 25 31




http://www.hammann.com/1960PS.txt

[dvtimes]

http://www.makezine.com/blog/archive/2005/08/puzzle_of_the_m.html

Comments
Oldest comments listed first.

SPOILER WARNING--------------

The house number is a red herring, as far as we're concerned. We don't know the house number. Therefore, all it serves to tell us is that the sum of the ages is an integer.

Assuming that each age given is an integer, there are several possibilities. However, we might further assume that at least one member of the house is not a minor. This restricts it to four possibilities for the age of the eldest--three if we assume a reasonable lifespan. (A gentleman of 225 years probably doesn't live with two infants.) But there's simply not enough information to provide a complete solution.

Sorry.

Posted by: dhasenan on August 24, 2005 at 05:22 PM

well, i think i solved it- but i'm waiting until mark posts the winner. the clue here was when the census taker asked "are you the eldest"...that's at least what i came up with.

Posted by: philliptorrone on August 24, 2005 at 05:35 PM

The problem states that 225 is the product of the ages of the three residents. Agreed that the house number is a red herring.

Posted by: dcmoisan on August 24, 2005 at 06:18 PM

yes, n x n x n = product of the numbers which is 225- the ages of all 3 people, n + n + n = the sum of the ages, the house number. the house number didn't seem inportant to me, other than it is a whole number, the question the census taker did ask, was relevant for my guess.

Posted by: philliptorrone on August 24, 2005 at 06:23 PM

I guess this is the root of all the grade school extra credit math questions, except the product is 225 instead of 36 :)

Posted by: VinnyF on August 24, 2005 at 06:29 PM

The house number isn't a red herring. Even though the census taker knows the house number, he must still ask one question to determine what the ages are.

Posted by: evandelay on August 24, 2005 at 06:38 PM

I agree with evandelay. There is only two possible combinations that would produce 225 as the product and have the same sum. The census taker's clarification question allows you to decide which of those two is correct.


At least, that is how I see it.



Here's a hint: The house number is 31.


Posted by: dhovis on August 24, 2005 at 06:55 PM

Well, I think there are 4 possible solutions. The "house" number is inconsequential.

Posted by: kebinator on August 24, 2005 at 07:48 PM

The specific house number is not important per se, but the fact that the census taker could not deduce the ages by knowing the house number allows us to solve the puzzle. We can use this fact to decide which of the two sets of ages that have the same product (31, as stated by dhovis) is the set we're after. Good luck!

Posted by: foofaa on August 24, 2005 at 08:11 PM

... "have the same sum", not "have the same product". Sorry!

Posted by: foofaa on August 24, 2005 at 08:15 PM

there is no red herring. the key thing to know is that the census taker KNOWS the house number and needs the last bit of info. also there's a bunch of intrinsic stipulations to the puzzle that need to be taken into account (the puzzle is published 45 years ago after all).

Posted by: gmania on August 24, 2005 at 10:12 PM

I just read this one this morning (8 o'clock in Paris, France). It sounds like a classical math puzzle. Since the guy needs more information than just the number of the house, it meens that several solutions exists with this number.



The only sum with several possible products is 31:


1) a 25 adult and twins aged 3


2) a baby aged 1 and teen twins aged 15



We know there is a "eldest", so the only solution is #1.



The 3 people are aged 3, 3, 25!



Papydom







Posted by: Papydom on August 25, 2005 at 12:05 AM

It’s all about prime factorization. You don't have to know any weird trivia about census taking circa 1960. If you want to see the solution look at http://www.hammann.com/1960PS.txt

Posted by: phammann on August 25, 2005 at 12:06 AM

The house number could be 35, with ages of 1, 9 and 25, couldn't it?
I know it's the 60's but they were supposed to be swinging.......

Posted by: akrycek on August 25, 2005 at 02:07 AM

1*3*3*5*5=225

so the combinations are

1*(3*5)*(3*5)=225 >>> 1 15 15

and
3*5*(3*5)=225 >>> 3 5 15

which is the right one since there cannot be two 15years old twins,
only one person is the eldest.

Posted by: marco_andreetta on August 25, 2005 at 02:43 AM

btw the house number is 23 but it doesn't mean anything :)

Posted by: marco_andreetta on August 25, 2005 at 02:45 AM

A possible answer is that the three occupants of the house are 3, 5 and 15. House number is 23 but it matters not.

3x5x15=225
3+5+15=23
15 year old is answering door

The puzzle doesn't imply any adults are involved or that a normal family structure is present... so there are 3 kids in the house. Big whoop.

I'm not sure why this is really a puzzle at all. Just pick three numbers that multiplied together will equal 225. Obviously there is a 5 involved and the rest just follows.

Posted by: Kevbo on August 25, 2005 at 03:20 AM

Several people are in error if they believe that the information provided is not relevant. The house number and the question "are you the eldest?" are important.

The only possible combinations of the three ages that give a product of 225 are:

1 1 225 Eldest too old total = 227
1 3 75 Possible total = 79
1 5 45 Possible total = 51
1 9 25 Possible total = 35
1 15 15 Unlikely as where is the parent total = 31
3 3 25 Possible total = 31
3 5 15 Unlikely as where is the parent total = 23
5 5 9 Unlikely as where is the parent total = 19

Unlikelies are possible, given that this is a Maths puzzle, not real life. So, given that we do not know the house number, but the census taker asks the age, we must have a house number that can be a result of two sets of three ages. If there was only one set that could produce the house number, he would not have had to ask. So, it is either 1 15 15 or 3 3 25. Given that he asks are you the eldest, and the first set would have two the same age, it must be 3 3 25

This would make sense, as the two three year olds are probably not up to:
1) answering the door
2) knowing what a product is or even what the house number is
3) shouldn't talk to strangers anyway

Dr. Mike Reddy, Wales, UK and a Make Reader!!!

Make is where I heard about the puzzle.

Posted by: mreddygbr on August 25, 2005 at 03:39 AM

P.S. I did this in 5 minutes, using excel to generate the combinations. After that it was mostly psychology. I did not look at the solution until just now, but feel happy that I hit it on the head!

Posted by: mreddygbr on August 25, 2005 at 03:41 AM

Finding your puzzle via Make magazine my answer is:

two 3 year olds and a 25 year old.

Solution is based on this:
Breaking 225 in primes the basis of the product is:

1x3x3x5x5 = 225
making groups of three of it results in
1+9+25=35
3+3+25=31
9+5+5= 19
1+15+15=31
3+5+15=23

Since only two housenumbers are double (31), this is what the census doubted about. With a 15 year old twin, the answer of being the oldest would have made no sense, so the family contains of a three year old twin ana a 25 year old parent.


Posted by: Radiator on August 25, 2005 at 05:02 AM

I completely disagree with those who say "With a 15 year old twin, the answer of being the oldest would have made no sense".
Just because people are twins doesnt mean they were born at the same time. One is older. And there is nothing that denotes that they are twins, perhaps at the time of the census the two are the same age even though their births are seperated by many months. If the ages were 3,3,25 then whomever cannot tell a 25yr from a 3yr will not solve this. Therefore, I think an answer of 1, 15, 15 makes more sense.

Posted by: colonel_colon on August 25, 2005 at 06:21 AM

Those who have decided they know the answer is 3, 3, 25 and the house number is 31, how did you eliminate the following possibilities:



1,3,75 (house number 79)

1,5,45 (house number 51)

1,9,25 (house number 35)

3,5,15 (house number 23)



???



It seems like we don't have enough information (or I'm not gleaning enough information out of the clues...)

Posted by: speedeep on August 25, 2005 at 07:14 AM

the other possibilities are discounted since they all have unique sums (i.e. only one product adds up to this sum). If this were the case the census taker would know everything by looking at the house number. The fact that he has to ask for more information means that the house number is not enough - i.e. there must be more that one possible solution that adds to the house number. The only possibilities that have the same sum are:

A) 15+15+1=31
B) 25+3+3=31

Knowing that there is an eldest person means that there can't be two oldest people with the same age, discounting A. Therefore the answer is B.

Posted by: nodemons on August 25, 2005 at 09:13 AM

the other possibilities are discounted since they all have unique sums (i.e. only one product adds up to this sum). If this were the case the census taker would know everything by looking at the house number. The fact that he has to ask for more information means that the house number is not enough - i.e. there must be more that one possible solution that adds to the house number. The only possibilities that have the same sum are:

A) 15+15+1=31
B) 25+3+3=31

Knowing that there is an eldest person means that there can't be two oldest people with the same age, discounting A. Therefore the answer is B.

Posted by: nodemons on August 25, 2005 at 09:14 AM

"the other possibilities are discounted since they all have unique sums.... The only possibilities that have the same sum are: A) 15+15+1=31 B) 25+3+3=31 Knowing that there is an eldest person means that there can't be two oldest people with the same age, discounting A. Therefore the answer is B.
Posted by: nodemons on August 25, 2005 at 09:14 AM"

The only problem I have with this is a sociological one. Was it considered legal for a 15 year old (or in this case 15 year old twins) to live as adults in a house in 1960? If the puzzle were posited today we would have to discard the any solution that resulted in the higest age being less than at least 16, if not 18. In 1960 I can imagine that it would be possible in some states but not others?
Or was the age of consent (thus marriage, with the older of the pair dying or abandoning his child bride to raise the two children, or her twin sibling and child) uniformly 15 or below in all states during the 1960's?

Wouldn't the census taker be compelled to report the situation to welfare authorities?

Posted by: NickCarter on August 25, 2005 at 10:45 AM

:o)

And I suppose the 'family' should report the census taker for not doing his job properly - surely he should be taking more information than the ages of people living there...

Posted by: nodemons on August 25, 2005 at 01:01 PM

Here is a link to the 1960 census:
http://www.census.gov/pubinfo/www/photos/Histforms/1960/His60FQ.html

He sure wasn't doing his job!

Posted by: NickCarter on August 25, 2005 at 01:22 PM

A few points:



1. A census taker. Didn't say who the census was for. So it may not have been a goverment census taker.



2. Doesn't say it was a census being taken in the US.



3. Two 15 year olds wouldn't necessarily be twins. They could be married to each other or a whole range of other possibilities.



4. I have a real problem with asking, "Are you the eldest?" to find out if a person is either 15 or 25 years old. If I was a 15 year old in a household of 3 people including another 15 year old a few months younger than I am and a 1 year old and someone asked me if I was the eldest person living there, you KNOW I would answer yes. So I don't think the person's answer should really mean anything.

Posted by: zenock on August 25, 2005 at 02:46 PM

[wankmaster]

Yes, good puzzle. Fair cop.

To split hairs tho, twins are never the same age, unless the mother had two fannies and they agreed to "cross the line" hand in hand, one would always be older than the other.

[wankmaster]

Seems that it is a known medical condition.

http://www.ffwdweekly.com/Issues/2005/1124/messy.htm