Mark posted a fun puzzle from the April 1960 issue of Popular Science. Head on over to BoingBoing and solve it- it would be great to have a MAKER solve it first! Link.
56 thoughts on “Puzzle of the Month: Popular Science, April 1960”
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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.
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.
The problem states that 225 is the product of the ages of the three residents. Agreed that the house number is a red herring.
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.
I guess this is the root of all the grade school extra credit math questions, except the product is 225 instead of 36 :)
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.
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.
Well, I think there are 4 possible solutions. The “house” number is inconsequential.
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!
… “have the same sum”, not “have the same product”. Sorry!
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).
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
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
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…….
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.
btw the house number is 23 but it doesn’t mean anything :)
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.
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.
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!
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.
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.
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…)
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.
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.
“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?
: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…
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!
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.