CAUTION:  ANSWERS DISCUSSED BELOW.  USE YOUR BRAIN AND DO NOT READ PAST THIS POINT UNTIL YOU FIGURE IT OUT.



This problem can be solved to answer the question exactly as it is stated, and the answer is provable.

We were given this problem as part of an Ed. Psy. class.  It wasn't graded, it was just to get us thinking.  I didn't get it because I was thinking about the problem the wrong way.

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A conversation took place between two friends, a philosopher and a mathematician, who had not seen or heard from one another in years.  The mathematician, who had exceedingly good memory, asked the philosopher how many children he had.  The philosopher replied that he had three.  The mathematician then asked how old the children were.  His friend, who knew how much mathematicians enjoy puzzles, said he would give a number of clues to his children's ages.

The philosopher's first clue:  "The product of the children's ages is 36."  The mathematician immediately replied that this was insufficient information.  The philosopher's second clue:  "All of the children's ages are integers, none are fractional ages, e.g., 1 1/2 years old."  Still the mathematician could not deduce the correct answer.

The philosopher's third clue:  "The sum of the children's ages is identical to the address of the house where we played chess together often, years ago."  The mathematician still required more information.  The philosopher then gave his fourth clue:  "The oldest child looks like me."  At this point, the mathematician was able to determine the ages of the three children.

This is the problem:  What were their ages and what was the mathematician's reasoning?

Yep, solved it.

Quoted: Yep, solved it. *link fixed to be broken*

Hey, that's cheating.  Let people solve it themselves.  If you give the answer people will just look there.

Damnit Tras, I was almost there and the temptation was too great.

I didn't have time to solve it, and so looked up the answer.  The reasoning to exclude certain options on the "oldest" child information is not true.

Quoted: I didn't have time to solve it, and so looked up the answer.  The reasoning to exclude certain options on the "oldest" child information is not true.

Why not?

Quoted: Quoted: I didn't have time to solve it, and so looked up the answer.  The reasoning to exclude certain options on the "oldest" child information is not true. Why not?

What if the answer is 6, 6, and 1 with the two six year olds being female and the one year old being male. Then the youngest would look more like him.

Thst sure appears to be written by a stereotypical psych educator who never made it past Calc 101.  Are your classmates a product of the "new" math in which estimating, self-esteem, and pharmacology are more important than correct answers?  

Assumptions are made, such as that the mathmatician would remember the house number because of an "exceedingly good memory" but that is not stated.  Twins are assumed to be the same gender and to have emerged from the birth canal simultaneously.  The philosopher is assumed not to be lying to the mathmatician, or engaging him in a more subtle puzzle in which the children are hypothetical.

ARRRGH!  You guys apparently did not catch the part where the philosopher said that the ages were integers, NOT fractions!  Therefore, if there are sets of twins and another baby, and he said that the oldest looks like him (keyword "oldest), it would have to be the child that is NOT a twin!  If the child who was not a twin was younger than the twins, there would not be a single oldest child.

Quoted: What if the answer is 6, 6, and 1 with the two six year olds being female and the one year old being male. Then the youngest would look more like him.

He said the OLDEST looked like him.  Not the YOUNGEST.

Quoted: Thst sure appears to be written by a stereotypical psych educator who never made it past Calc 101.  Are your classmates a product of the "new" math in which estimating, self-esteem, and pharmacology are more important than correct answers?   Assumptions are made, such as that the mathmatician would remember the house number because of an "exceedingly good memory" but that is not stated.  Twins are assumed to be the same gender and to have emerged from the birth canal simultaneously.  The philosopher is assumed not to be lying to the mathmatician, or engaging him in a more subtle puzzle in which the children are hypothetical.

Why do you have to read so much into it?  Just take it word for word.  Geez.

The reason the "exceedingly good memory" information was given was so that it would be used.  The story does not give useless info, so any info given should be used.
The philosopher did not say that the twins emerged simultaneously.  He said that the ages are integers.  In other words, if you assume the ages are integers, the hints will lead you to the right answer.
And of course you assume that the philosopher is telling the truth.

They were triplets, all are 12 years old, the oldest of the 3 look likes the old man......did I fail?

Quoted: They were triplets, all are 12 years old, the oldest of the 3 look likes the old man......did I fail?

Yup, you fail

12*12*12 != 36

Twins can not be born simultaneously, even via C-section birth.  One is always the older, if only by seconds.  This being the case, then how can twins be excluded based on the explanation?  If each age is expressed as an integer, then a twin's age may be expressed in that fashion, even if one is rounding, slightly.

If one insists that no rounding to integers is occuring, then one must surmise that all three children were born at the same diurnal time, and that time was the time when the second clue was given.

Quoted: Twins can not be born simultaneously, even via C-section birth.  One is always the older, if only by seconds.  This being the case, then how can twins be excluded based on the explanation?  If each age is expressed as an integer, then a twin's age may be expressed in that fashion, even if one is rounding, slightly. If one insists that no rounding to integers is occuring, then one must surmise that all three children were born at the same diurnal time, and that time was the time when the second clue was given.

???

I already explained this.  Another way of putting what he said is that if you assume the ages are integers, you can deduce the answer.  He did not say that the babies were born at the exact same time.

2, 3 & 6 is what I came up with.

2*3*6=36

The rest is useless info.

Quoted: 2, 3 & 6 is what I came up with. 2*3*6=36 The rest is useless info.

But can you prove it?

Hint:  THe rest is not useless info.

I came up with a fewsolutions but I dont know which one WITHOUT the house number of where they played chess... didnt say.

Using Shorty's logic... was the house Number 11?

3,3 and 4?

2, 3, and 6.
Where all three played years ago is a key statement.
It means that the youngest must be mulitple ages old.
Minimum of 2
2, 3, and 6 is the only combination that works with the minimum age of 2.
Minimum age of 3 or more won't work.
Assumes no twins.

Quoted: Quoted: What if the answer is 6, 6, and 1 with the two six year olds being female and the one year old being male. Then the youngest would look more like him. He said the OLDEST looked like him.  Not the YOUNGEST.

Yes he did. Ok then one of the twins is a boy and the other a girl. The "oldest" still looks like him, but the other oldest does not.