(no subject)
Aaron Koller
gave it to me were just idiots making too many assumptions...
A person is trying to find the ages of the children next door. The three
children tell their neighbor that the product of their ages is 36 and the
sum of their ages is equal to their address number. The neighbor looks
at the address and tells them he doesn't have enough information to find
their ages. So the children say "The oldest one of us likes chocolate
pudding" and then the neighbor knew their ages. What were they?
--
Aaron Koller | "In this house we obey the laws of thermodynamics!"
1582...@msu.edu | - Homer Simpson
Keith F. Lynch
Aaron Koller <1582...@msu.edu> wrote:
> A person is trying to find the ages of the children next door. The three
> children tell their neighbor that the product of their ages is 36 and the
> sum of their ages is equal to their address number. The neighbor looks
> at the address and tells them he doesn't have enough information to find
> their ages. So the children say "The oldest one of us likes chocolate
> pudding" and then the neighbor knew their ages. What were they?
2, 2, and 9.
Spoiler:
Here are all the possible combinations of three ages whose product
is 36, together with their sum:
1 1 36 38
1 2 18 21
1 3 12 16
1 4 9 14
1 6 6 13
2 2 9 13
2 3 6 11
3 3 4 10
Since the neighbor didn't have enough information to determine their
ages even after knowing the address number, the address number must
have been 13, since that's the only one which occurs twice in the
table.
1 6 6 13
2 2 9 13
When it was mentioned that there was an oldest child, that showed it
had to be entry with the two oldest ages unequal.
2 2 9 13
Assumptions: Ages are always postive whole numbers (plausible).
The neighbor always makes all possible correct deductions from the
available facts (implausible, but conventional in problems such as
these). A child would not be referred to as "oldest" if the child
had the same whole-number age as a sibling (very implausible, whether
they were twins or whether they were born 11 months apart).
Ralph Ray Craig
>I'm not sure if this puzzle has a logical answer or if the people that
>gave it to me were just idiots making too many assumptions...
>
>children tell their neighbor that the product of their ages is 36 and the
>sum of their ages is equal to their address number. The neighbor looks
>at the address and tells them he doesn't have enough information to find
>their ages. So the children say "The oldest one of us likes chocolate
>pudding" and then the neighbor knew their ages. What were they?
>
SPOILER
The product of their ages is 36 which means that the
factors are 2 2 3 and 3. This leads to the following possibilities
for three ages:
2 2 9 sum of ages is 13
2 3 6 " 11
3 3 4 " 10
1 6 6 " 13
1 2 18 " 21
1 9 9 " 19
1 3 12 " 16
1 1 36 " 38 <--- Old Kid!
The only way that you could not yet have enough info
is if the apartment number is 13. By mentioning the
"oldest child" you know that the ages are not 1,6 and 6.
They must be 2, 2, and 9 years old, respectively.
(The nine-year old likes chocolate pudding;)
--
--
Ralph Craig |Esperanto parolata. INFO: el...@netcom.com, u...@erc.eur.nl
104-9 Horne St. |
Raleigh, NC 27607 | Mean people suck.
Send me a postcard,| "Every day is Lesbian Lovers' Day!" --seen on Friends
I'll send you one. | WILL PROVE THEOREMS FOR FOOD
Chris Cole
>I'm not sure if this puzzle has a logical answer or if the people that
>gave it to me were just idiots making too many assumptions...
>
>A person is trying to find the ages of the children next door. The three
>children tell their neighbor that the product of their ages is 36 and the
>sum of their ages is equal to their address number. The neighbor looks
>at the address and tells them he doesn't have enough information to find
>their ages. So the children say "The oldest one of us likes chocolate
>pudding" and then the neighbor knew their ages. What were they?
>
==> logic/children.p <==
A man walks into a bar, orders a drink, and starts chatting with the
bartender. After a while, he learns that the bartender has three
children. "How old are your children?" he asks. "Well," replies the
bartender, "the product of their ages is 72." The man thinks for a
moment and then says, "that's not enough information." "All right,"
continues the bartender, "if you go outside and look at the building
number posted over the door to the bar, you'll see the sum of the
ages." The man steps outside, and after a few moments he reenters and
declares, "Still not enough!" The bartender smiles and says, "My
youngest just loves strawberry ice cream."
How old are the children?
A variant of the problem is for the sum of the ages to be 13 and the
product of the ages to be the number posted over the door. In this
case, it is the oldest that loves ice cream.
Then how old are they?
==> logic/children.s <==
First, determine all the ways that three ages can multiply together to get 72:
72 1 1 (quite a feat for the bartender)
36 2 1
24 3 1
18 4 1
18 2 2
12 6 1
12 3 2
9 4 2
9 8 1
8 3 3
6 6 2
6 4 3
As the man says, that's not enough information; there are many possibilities.
So the bartender tells him where to find the sum of the ages--the man now knows
the sum even though we don't. Yet he still insists that there isn't enough
info. This must mean that there are two permutations with the same sum;
otherwise the man could have easily deduced the ages.
The only pair of permutations with the same sum are 8 3 3 and 6 6 2, which both
add up to 14 (the bar's address). Now the bartender mentions his
"youngest"--telling us that there is one child who is younger than the other
two. This is impossible with 8 3 3--there are two 3 year olds. Therefore the
ages of the children are 6, 6, and 2.
Pedants have objected that the problem is insoluble because there could be
a youngest between two three year olds (even twins are not born exactly at
the same time). However, the word "age" is frequently used to denote the
number of years since birth. For example, I am the same age as my wife,
even though technically she is a few months older than I am. And using the
word "youngest" to mean "of lesser age" is also in keeping with common parlance.
So I think the solution is fine as stated.
In the sum-13 variant, the possibilities are:
11 1 1
10 2 1
9 3 1
9 2 2
8 4 1
8 3 2
7 5 1
7 4 2
7 3 3
6 6 1
6 5 2
6 4 3
The two that remain are 9 2 2 and 6 6 1 (both products equal 36). The
final bit of info (oldest child) indicates that there is only one
child with the highest age. This cancels out the 6 6 1 combination, leaving
the childern with ages of 9, 2, and 2.
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Jane Pook
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>Aaron Koller <1582...@msu.edu> wrote:
>>I'm not sure if this puzzle has a logical answer or if the people that
>>gave it to me were just idiots making too many assumptions...
>>
>
>The only way that you could not yet have enough info
>is if the apartment number is 13. By mentioning the
>"oldest child" you know that the ages are not 1,6 and 6.
>They must be 2, 2, and 9 years old, respectively.
>(The nine-year old likes chocolate pudding;)
The trouble is that in real life, 6 years old is not a single point.
Any child between the ages of 6 years and 6 years and 364(approx) days
is called "6". It's very easy to imagine that a woman has a child
and becomes pregnant almost immediately - within 3 months is possible.
Not to mention twins - one is always older except in the
unusual case that they were born by Caesarian section and taken out at
precisely the same moment.
So, although it sounds quite good mathematically and is a nice logic
puzzle, if you're being pedantic and realistic then it doesn't work.
So the person who can't get it may not be stupid, they just may be
more focussed on the real world than on mathematics. Of course, that
probably doesn't apply to anyone reading here!
Chris Lusby Taylor
>
<actual puzzle snipped>
> Assumptions:...A child would not be referred to as "oldest" if the child
> had the same whole-number age as a sibling (very implausible, whether
> they were twins or whether they were born 11 months apart).
Hmmm. My only children are twins. Although one is very proud that he is
the older (by five minutes) I would never refer to him as my older child.
He might, though!
Chris Lusby Taylor