How Many Children Does the Man Have?

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Discussion Overview

The discussion revolves around a logic puzzle involving a man and the number of children he has, based on clues provided about the total number of children, the distribution among families, and a specific home number. Participants explore various interpretations and calculations related to the puzzle, including the implications of the clues given.

Discussion Character

  • Exploratory
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants propose that the man has 5 children based on the information provided.
  • Others question whether it is possible for the man to have 6 children, indicating a lack of clarity in the reasoning.
  • A participant suggests that the home number could be interpreted in various ways, leading to confusion about its relevance.
  • Some participants discuss the importance of the guest's question regarding the smallest family's number of children, suggesting it eliminates several possibilities.
  • There is a debate about whether the puzzle can be solved without certain cultural assumptions regarding the home number.
  • Several participants calculate potential products of the number of children and explore combinations that fit the criteria given in the puzzle.
  • One participant notes that the guest's ability to determine the number of children hinges on the uniqueness of the solution based on the clues provided.
  • Another participant reflects on the nature of the puzzle, comparing it to other logic problems and expressing frustration over the multitude of potential solutions.
  • Some participants identify specific combinations of numbers that could represent the families' children, discussing their products and sums.
  • A later reply suggests that the only viable solution involves the smallest family having more than one child, leading to a definitive answer of 5 children for the man.

Areas of Agreement / Disagreement

Participants express differing views on the number of children the man has, with some asserting he has 5, while others believe 6 could also be a possibility. The discussion remains unresolved regarding the implications of the home number and the uniqueness of the solution.

Contextual Notes

Participants note that the puzzle's solution may depend on specific cultural interpretations of the home number and the assumptions made about the distribution of children among families. There are also unresolved mathematical steps and combinations that lead to multiple potential answers.

Who May Find This Useful

Individuals interested in logic puzzles, mathematical reasoning, and problem-solving strategies may find this discussion engaging.

Werg22
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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?
 
Last edited:
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Werg22 said:
How many children does the man in question have?
He has 5 children.
:smile:
 
I'm missing a piece. I don't see why he couldn't have 6.
 
DaveC426913 said:
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?
 
Rogerio said:
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.
 
Dave, it's important to remember the question the guest asks.
 
Werg22 said:
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.
 
It's definitely solvable :wink:
 
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?
 
  • #10
Well, according to your calculations, how much is the product of the number of children in each family?
 
  • #11
Rogerio said:
Well, according to your calculations, how much is the product of the number of children in each family?

Either 120 or 180 or 240.
 
  • #12
Hm. No, I'm definitely doing something wrong. Upon review, my notes reveal a plethora of answers. I'm missing several pieces.
 
  • #13
DaveC426913 said:
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?
 
  • #14
Rogerio said:
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.
 
  • #15
DaveC426913 said:
2,3,5,6 works.
No, it doesn't. Answer the post #13, and you will see why it doesn't work.
 
  • #16
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
 
  • #17
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").
 
  • #18
DaveC426913 said:
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!:smile:
 
  • #19
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."
 
  • #20
DaveC426913 said:
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.
 
  • #21
Werg22 said:
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.
 
  • #22
Dave, you do realize that the fact that the guest does know the home number is very important, right?
 
  • #23
Werg22 said:
Dave, you do realize that the fact that the guest does know the home number is very important, right?
No.
10 chars
 
  • #24
Well, start realizing!
 
  • #25
I think I'd better leave this for those more skilled.
 
  • #26
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"?
 
  • #27
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!
 
  • #28
Dave, could you give me two examples of your solutions?
 
  • #29
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.
 
  • #30
Now neutrino, are there solutions that have the same product?
 

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