Puzzle of the Day: How did he find the age of the children?

I have never cared much for the "standard" answer to this puzzle,

based on a "youngest" or "oldest" child ruling out some case involving twins.

The essence of the problem is:

Possible ways to factor 72 into 3 factors:

1,1,72 = 74 (sum)

1,2,36 = 39

1,3,24 = 28

1,4,18 = 23

1,6,12 = 19

1,8,9 = 18

2,2,18 = 22

2,3,12 = 17

2,4,9 = 15

2,6,6 = 14

3,3,8 = 14

3,4,6 = 13

The only ambiguous sum is 14,

with the ages 2,6,6 or 3,3,8,

and everything else ruled out.

But a reference to a youngest (or oldest) child doesn't really help,

because even with biological twins born minutes apart,

one is slightly older than the other, so there is always

a unique youngest (or oldest) child.

Also, two separately-born siblings could be born less than a year

apart, and be the same age for a short time near the the start of the year.

With adopted or foster children, they could be even closer in age.

If 2-year-olds do not go to school, but 3-year-olds do,

then this version would distinguish those two cases,

but in other versions that I have seen the mention of

the (usually) oldest child does not offer such information.

(the child is sick, or likes ice cream, or what have you)

A good discussion can be found here,

with another variation on the clue about oldest/youngest:

http://mathforum.org/library/drmath/view/58492.htm...

That one discusses the fact that even when there are twins

there is always an oldest/youngest child in the family.

There is also a Wikipedia page about it:

http://en.wikipedia.org/wiki/Ages_of_Three_Childre...

which also describes a version where the product is 36

rather than 72.

The puzzle, and sometimes the solution as well,

can be found on many other sites, too.

It's quite popular.

This is a very old problem, cited in Martin Gardner books and many other sources. The answer is 2, 6 and 6 - from several possible ways to factor 72 into 3 factors only in

72 = 2 * 6 * 6 = 3 * 3 * 8

the factors add up to 14 and the milestone number 14 doesn't provide a clue.

P.S. (Note to Raj Kish) How should we solve the puzzle if instead of "My youngest child is yet to go to school..." YM had said for example "My oldest child likes ice cream very much!" and the rest of the discussion the same?

P.S.(2) No Raj, the answer then would be 3, 3, 8, think it over again.

Final remark: MathMan TG has submitted an excellent explanation of this trivial problem, read it carefully. The intention of its author has been clearly to offer a representation in a fancy dress of the following arithmetical problem: factor 72 into 3 factors - natural numbers, if knowing the sum of the factors is not sufficient to determine them and among them the least factor is unique.

The answer is 72 = 2 * 6 * 6 and the rest discussion is a waste of time.

This is a Mathematical Forum, isn't it? Or we should discuss educational or biological issues or world financial crisis here?

One other possible way for 72 to be factored into three is 3,4 and 6.And to me this sounds a better way for YM to have posed the problem because he made no mention of his having twins.And the additional detail about the milestone is just to

mislead for it provides no clue.The whole solution boils down to factoring 72 into the number of children so as to provide for the three factors to obtain a product of 72.Of course one other fact needs to be borne in mind which is that YM's youngest child is yet to start going to school.So,the youngest child cannot be more than three years old,because if it is then the lowest factor would be 4 which would put the other two children at ages above 4 which will nevr provide for the product of 72 for the the ages of the three children.Two other possible answers are 2,4,9

and 1,6 and 12 apart from the one given by my predecessor viz. 2,6 and 6.

3,3 and 8 is eliminated because YM said "My youngest child-----"

Have a Good Day.

Edit:-Sorry,I missed out one more factor in which case there is one more possible answer viz.1,4 and 18.

Mr."Duke",The clue suggested by you would only increase the number of possible answers and include the one I have posted under "Edit" because,ice cream is loved by all children and adults.There are very few people who do not like ice cream.You too have a good day,sir.

Mr."Duke",I still insist that 3,3,and 8is eliminated because Y M did not mention "My

Youngest CHILDREN but My Youngest CHILD (singular).

As someone who works in a college, I shouldn't say this yet I recommend that you bypass with Bob's answer. As for the raging debate about if Autism is an academic or a medical diagnosis, the answer is its both. in case you want a medical or medical diagnosis of autism, you should have a finished (and muy expensive) evaluation performed by skill of a psychologist who specialzes in this section. The evaluation might want to not be a 10 minute waiting room eyeball of the toddler yet an intensive evaluation (cognitive ability, sensory aspects, speech, language, habit, adaptive habit). the ultimate evaluation would also include the Autism Diagnostic commentary time table which gadgets up social situations designed to elicit behaviors instantly ahead to little ones with autism. in case you opt for an academic eligibility, you should let the faculty do the evaluation. the possibilities are extreme, it isn't likely as rigorous or thorough. maximum college psychologists are literally not experienced specially in diagnosing autism (although there are some like me who're). The up-area is this evaluation will be loose. Clinically, it sounds extra like your son would have asperger's syndrome instead of the classic autism because his language is wisely stepped ahead. the criteria for it truly is that incorporates difficulty with social interplay and some sort of repetitive habit and restricted pastime. base line, i'd let the faculty do the evaluation because it truly is loose. it truly is probable they are going to eyeball your toddler and use some checklists. in case you do not experience mushy with that, then i'd refuse to signal the IEP place of work artwork and demand that an self sufficient evaluation be performed (on the faculty's rate). Use the recommend besides.

i wonder some link is missing

you have provided x*y*z = 72

but have not provided x+y+z (the mile stone details)

z may be 2 or 3

this may be the reason both the answerers have given their answers basing on permutations and combinations , (either or )but unable to correctly mention the answer

In our locality children of 3 years old are send to school☺

so the youngest child maybe 1 or 2 years of old

& other's ages are from 3 onwards-----------since both of them are schooled

possible sets of ages of children

{(1 , _ , _ )}={(1,6,12),(1,8,9),(1,4,18),(1,3,24)}---by factorising 72 into two factors >_3

{(2, _ , _ )}={(2,3,12),(2,4,9),(2,6,6)}------by factorising 36 into two factors >_3

you just vaisting your time,even I am when answring ,but I hope for next time ask only how much people can read .