How Many Children Does the Man Have?

[Werg22]

A man invites his friend to his house for a small chatter over some tea. There is a good number of children playing in the backyard, and upon seeing this, the guest asks his host whether all these children are his. The host gives him a brief "no" and tells him that the children belong to himself and three other families. The guest redoubles curiosity and asks to his host how many children he has. The host answers him: "Let's put it this way: the total number of children playing in the background is less than 18, with each family having a different number of children, mine being the largest. Also, the product of the number of children in each family happens to be my home number which you just saw when you arrived". The guest then scrambles on piece of paper for a bit and then looks up and says "I need more information. Does the family with the smallest number of children have more than one child?". As soon as the host answers, the guest is able to correctly tell how many children the latter has. All of this having been said, anyone can do the same on the basis of the information given above. How many children does the man in question have?

 

[Rogerio]

How many children does the man in question have?

He has 5 children.

 

[DaveC426913]

I'm missing a piece. I don't see why he couldn't have 6.

 

[Rogerio]

I'm missing a piece. I don't see why he couldn't have 6.

And what would be the home number, in this case?

 

[DaveC426913]

And what would be the home number, in this case?

Well, I didn't really know what that meant. Address? Phone number? My phone number is ten digits.

 

[Werg22]

Dave, it's important to remember the question the guest asks.

 

[DaveC426913]

Dave, it's important to remember the question the guest asks.

Yes, the way I see it, that eliminates 9 out of 12 possibilites, narrowing it down to 3.

 

[Werg22]

It's definately solvable

 

[DaveC426913]

Is this relevant? "my home number which you just saw when you arrived".
I don't see how that provides any information for filtering. At least not a universal one. Perhaps it's Yankee-centric?

 

[Rogerio]

Well, according to your calculations, how much is the product of the number of children in each family?

 

[DaveC426913]

Well, according to your calculations, how much is the product of the number of children in each family?

Either 120 or 180 or 240.

 

[DaveC426913]

Hm. No, I'm definitely doing something wrong. Upon review, my notes reveal a plethora of answers. I'm missing several pieces.

 

[Rogerio]

Either 120 or 180 or 240.

If it was 180, for instance, the numbers would have to be a combination of the factors
2*2*3*3*5.
Considering the possibility of a family with just 1 child, how many children would the other families have?

 

[DaveC426913]

If it was 180, for instance, the numbers would have to be a combination of the factors
2*2*3*3*5.

2,3,5,6 works.

 

[Rogerio]

2,3,5,6 works.

No, it doesn't. Answer the post #13, and you will see why it doesn't work.

 

[DaveC426913]

If family A had just one child, then the possibilities are virtually limitless.
1,2,3,4
1,2,3,12
1,4,5,7
or anything in between

 

[DaveC426913]

The question here isn't whether it's solvable, the question is whether it's solvable without certain culture-centric conventions (such as certain values for a "home number").

 

[Rogerio]

If family A had just one child, then the possibilities are virtually limitless.
1,2,3,4
1,2,3,12
1,4,5,7
or anything in between

If the product is 180, and one family has one children, how many children would the other families have?
For instance, 4,5,9 doesn't works, since the sum 1+4+5+9 > 18 ...

Hint: reread the original question!

 

[Werg22]

Dave, your not concluding the most out of this part: "As soon as the host answers, the guest is able to correctly tell how many children the latter has."

 

[Rogerio]

The question here isn't whether it's solvable, the question is whether it's solvable without certain culture-centric conventions (such as certain values for a "home number").

Forget the "home number". Consider it was just a number written in a piece of paper.

 

[DaveC426913]

Dave, your not concluding the most out of this part: "As soon as the host answers, the guest is able to correctly tell how many children the latter has."

Yeah, there're only two possibilities, either the smallest family has 1 or it has more. That means at least one of those conditions has only one solution. As soon as he knows it's that one, he knows the answer.

 

[Werg22]

Dave, you do realize that the fact that the guest does know the home number is very important, right?

 

[DaveC426913]

Dave, you do realize that the fact that the guest does know the home number is very important, right?

No.
10 chars

 

[Werg22]

Well, start realizing!

 

[DaveC426913]

I think I'd better leave this for those more skilled.

 

[Werg22]

Dave... what I am trying to do is to get you to ask yourself the question "Are there 4 different numbers whose sum is less than 18 and that when multiplied together give a product that can be written as the product of a or many different set of 4 numbers, this keeping in mind that either a. All sets but one have the number 1 as the least number or b. Only one set has 1 as the least number"?

 

[DaveC426913]

Yeah, I'd realized that was the kicker. When the guest asks the yes/no question, it's because one of the two possibilities has only one solution.

And I know that this is that it is very "lucky"; the only reason the guest CAN figure it out is because it is THIS set of numbers. With virtually any other set of numbers, the guest would not have enough info.*

But I'm missing a pertinent piece. I get way too many solutions. And I guess my brain doesn't feel like concentrating.

* this always bugged me about Sherlock Holmes too. The tobacco the villain smokes is always unique, and the beach he was on yesterday is ALWAYS the only one of its type in the world!

How does he solve crimes when the villains are just normal, non-eccentric, non-obsessive types? He doesn't!

 

[Werg22]

Dave, could you give me two examples of your solutions?

 

[neutrino]

2,3,4,5/6/7/8
2,4,5,6

Other possibilities with 1 as the least number has already provided by Dave in post #16. I have come across another version of the puzzle before (the characters were different), but I somehow felt that was easier.

 

[Werg22]

Now neutrino, are there solutions that have the same product?

 

[smaster]

I think I got it. Werg22 pushing us toward the right clue with every post he makes. I think I got it before I start reading second page. Here it is.
Guest knew the house number, that means he could eliminate some possibilities. But he needed more info.
Why? Because he had more than one possibility the product of which numbers gave him still the same house number. The way he asked his last question means that he had some possibilities with family A having 1 kid and with family A having more than 1 kid the product of which numbers would be equal.
Now let's see the possibilities with family A having more than 1 kid. There only 6 possibilities I found:
2345, 2346, 2347,2348, 2356, 2357, 2456. The product of which gives us 120, 144, 168, 192, 180, 210, 240 accordingly. I found only 2 possibilities starting with 1 kid and product of which numbers is matching with the product of my other 6 possibilities. It's 1456 and 1358. The product of these numbers gives us 120. Since the guest didn't need any more clues after his last question, there were more than 1 kid in family A (family with the lowest number of kids). That gives us the only one sequence of numbers 2345. The host has 5 kids.

 

[showup199]

wow that was great thinking!

 

[Newton86]

amazing