It's only important how many children the cousin has if the house number is 120, so that's the solution. 2,3,4,5.
</strong><hr></blockquote>
You got it. There are two 120's when the cousin has one child. So that fact that Dorothy could provide the correct answer means the cousin has two children. You forgot to mention that.
Good job Sherlock Holmes.
By the way, a few misread the puzzle again, so I made one last little revision, to make it more bullet proof.
Just thought about it again. There are some more solutions, e.g. if the house number is 144:
[code]
a) 1 2 6 12 b) 1 2 8 9 c) 1 3 4 12 d) 1 3 6 8 e)2 3 4 6
</pre><hr></blockquote>
a) impossible
b) the brother has one child with the cousin and two with the sister (= 17 children in the backyard)
c+d) same reasoning as b)
e) the only reasonable scenario
Of course, Dorothy already knew that b-d are highly unlikely but she still wanted to rule out incest. She was a very polite girl, so she asked: "Would you tell us whether there are one or two children in your cousin's family?" After that she could present the solution: 2,3,4,6
(BTW: I liked it the way it was before your last revision, now you exclude 3 and more children which is impossible of course, but people should have to find out first)
Just thought about it again. There are some more solutions, ...
</strong><hr></blockquote>
I confess that your alternate solution never crossed my mind. Now that is thinking outside the box! Good one. Regarding the wording, I just revised it again at your suggestion. The first problem I had was putting down a number like one, which expects a yes or no answer. People were looking for little clues to know which way the professor responded. Next, every little body language gesture had to have an unambiguous meaning. It had to be very clear what the professor's nod signified. It is a tough job to write clearly. I feel like I'm writing computer code, and should be giving them revision numbers. I guess this thread was the beta test.
The puzzle was solved a couple days ago by 123, but some may want a detailed explanation of the solution. So, here is a try at it:
There are two important pieces of information that allow the puzzle to be solved. First, Dorothy knew the house number. Second, she was unable to solve the problem without knowing how many children the cousin had. What that tells us is that the house number shows up at least twice, and shows up both were the cousin has one child, and where the cousin has two. (The cousin cannot have three, since the total number of children would exceed 17.)
So, to solve the problem, you must list all possible combinations of children along with a house number for each. It is best to organize these into two sets. One where the cousin has one child, and the other where the cousin has two children. Then look for duplications. Only the number 120 appears in both sets, so it must be the house number.
The last thing you need to figure out is the professor's answer. Did the cousin have one or two children? As it turns out, the number 120 shows up twice in the set where there is one child. If the professor's answer had been one child, Dorothy could not have solved the problem. The fact that she did solve it lets us conclude that there are two children in the cousin's family. Q.E.D.
Comments
for ($i = 1; $i*4 + 3 < 18; $i++) {
\tfor ($j = $i+1; $i+$j*3 + 2 < 18; $j++) {
\t\tfor ($k = $j+1; $i+$j+$k*2 + 1 < 18; $k++) {
\t\t\tfor ($l = $k+1; $i+$j+$k+$l < 18; $l++) {
\t\t\t\tprint $res[$i*$j*$k*$l] . " $i $j $k $l\
" if($res[$i*$j*$k*$l]);
\t\t\t\t$res[$i*$j*$k*$l] .= " $i $j $k $l";
}}}}
1 2 3 8 1 2 4 6
1 2 3 10 1 2 5 6
1 2 4 10 1 2 5 8
1 2 3 10 1 2 5 6 1 3 4 5
1 2 4 9 1 3 4 6
1 2 6 7 1 3 4 7
1 2 6 8 1 3 4 8
1 2 5 9 1 3 5 6
1 3 5 8 1 4 5 6
1 3 5 8 1 4 5 6 2 3 4 5
</pre><hr></blockquote>
It's only important how many children the cousin has if the house number is 120, so that's the solution. 2,3,4,5.
[ 01-31-2003: Message edited by: 123 ]</p>
<strong>
It's only important how many children the cousin has if the house number is 120, so that's the solution. 2,3,4,5.
</strong><hr></blockquote>
You got it. There are two 120's when the cousin has one child. So that fact that Dorothy could provide the correct answer means the cousin has two children. You forgot to mention that.
Good job Sherlock Holmes.
By the way, a few misread the puzzle again, so I made one last little revision, to make it more bullet proof.
[ 01-31-2003: Message edited by: snoopy ]</p>
[code]
a) 1 2 6 12 b) 1 2 8 9 c) 1 3 4 12 d) 1 3 6 8 e)2 3 4 6
</pre><hr></blockquote>
a) impossible
b) the brother has one child with the cousin and two with the sister (= 17 children in the backyard)
c+d) same reasoning as b)
e) the only reasonable scenario
Of course, Dorothy already knew that b-d are highly unlikely but she still wanted to rule out incest. She was a very polite girl, so she asked: "Would you tell us whether there are one or two children in your cousin's family?" After that she could present the solution: 2,3,4,6
(BTW: I liked it the way it was before your last revision, now you exclude 3 and more children which is impossible of course, but people should have to find out first)
<strong>
Just thought about it again. There are some more solutions, ...
</strong><hr></blockquote>
I confess that your alternate solution never crossed my mind. Now that is thinking outside the box! Good one. Regarding the wording, I just revised it again at your suggestion. The first problem I had was putting down a number like one, which expects a yes or no answer. People were looking for little clues to know which way the professor responded. Next, every little body language gesture had to have an unambiguous meaning. It had to be very clear what the professor's nod signified. It is a tough job to write clearly. I feel like I'm writing computer code, and should be giving them revision numbers. I guess this thread was the beta test.
[ 02-01-2003: Message edited by: snoopy ]</p>
There are two important pieces of information that allow the puzzle to be solved. First, Dorothy knew the house number. Second, she was unable to solve the problem without knowing how many children the cousin had. What that tells us is that the house number shows up at least twice, and shows up both were the cousin has one child, and where the cousin has two. (The cousin cannot have three, since the total number of children would exceed 17.)
So, to solve the problem, you must list all possible combinations of children along with a house number for each. It is best to organize these into two sets. One where the cousin has one child, and the other where the cousin has two children. Then look for duplications. Only the number 120 appears in both sets, so it must be the house number.
The last thing you need to figure out is the professor's answer. Did the cousin have one or two children? As it turns out, the number 120 shows up twice in the set where there is one child. If the professor's answer had been one child, Dorothy could not have solved the problem. The fact that she did solve it lets us conclude that there are two children in the cousin's family. Q.E.D.