Logic Question

OK, so the total is >= 9 and < 18. And there are at least two sets of numbers that, when multiplied together, have the same product, and one set of the numbers has a "1" - the sister question. A quick list of the possibilities leads to 6,5,4,1 and 5,4,3,2 as the two sets. The house number is 120, but like the math guy, I can't tell which set it is until I know about the sister.

You are right about the house number. You now have to rely on logic and do a little more work to determine how many children the sister has and which set would be correct.

I am impressed with your logic so far.

Why should I, as a lowly engineer, be expected to do more work than a mathematician?

Because!

Then I choose 5,4,3,2 - since the friend states that each family has a different number of children, the sister having the fewest. And the fewest children you can have is 2.

No, the fewest number would be 1. You cannot arbitrarily choose the answer, it must be backed up with logic. This indicates there is only one answer and that answer is provable. As a hint it is provable because the mathematician could not solve the problem until he knew if the sister had more than 1 child. Why?

Building on the same logic as bhankiii, I find that there are three sets with a product of 120. They are:

1, 3, 5, 8

1, 4, 5, 6

2, 3, 4, 5

The mathematician's friend must have answered, "more than one". Since there is only one choice of a set greater than one (2, 3, 4, 5), the mathematician could then make a choice. If the answer was "no, not more than one", The mathematician would have to ask another question to determine an answer.

Your logic is impeccable and correct! Going through all the sets totaling 10 and not more than 17 and finding the products of each set the only common product that is found in sets starting with 1 and sets starting with 2 is 120.

Since the product 120 appears twice in sets beginning with 1 and only once in sets beginning with 2 it is logical that set 2,3,4,5 is correct since the mathematician was able to solve after learning the number of children in the sisters family. If the sister had only one child then the mathematician would be unable to solve since there would be 2 possible answers.

Here's my idea of the solution:

There are 9 players in a baseball team. So they if they have enough players for one team but not 2, there must be a total of between 9 and 18 children. The friend has the most children and the sister the fewest...in saying this we can begin as follows, remembering that there is a different no. of children in each family:

No. of children in each family:

Friend: 4

Brother 1: 3

Brother 2: 2

Sister: 1

This is a total of 10 children (enough for one team but not 2).

Multiplying these out gives 24.

A second solution could be:

Friend: 5

Brother 1: 4

Brother 2: 3

Sister: 2

This is a total of 14 children (enough for one team but not 2).

Multiplying these out gives 120.

No other solutions are possible since any more children will allow the children to play baseball. So it seems both the above solutions are possible.

Yet the mathematician, after getting his first answer wrong, asks if the sister has more than one child. Upon hearing the answer he then gets the answer right.

So I'm guessing the second solution is right:

House number = 120!

Any other ideas??

cheers

There can not be less than 10 children (1+2+3+4=10) and there can not be more than 17 (not enough to make 2 ball teams). OK, so the mathematician obviously knows the house number and the number of children his friend has. He tries to determine the number of children in the other families such that the total of children in each family when multiplied together will equal the house number.

Nobody said the mathematician got a wrong answer. What is stated is he could not solve the problem until he found out how many children are in the sisters family. It is stated the sister had the fewest number of children. Could she have 3 children? No, because the smallest set of numbers would be 3+4+5+6=18 which is enough to make 2 ball teams and it is stated they did not have enough children to make 2 teams.

Therefore the sister had to have at least 1 but not more than 2 children. The solution to this is not a guess. It is provable via logic.

It seams that your answer lies in interpretation of question itself. Since all of them have children none have only a child,

That way the best suitable answer is 2, 3, 4, &5 and house number is 120.still I shell say grammar is never as logical as of mathematics.

If asked how many children you have the answer could be 1 child. The question deals with logic, not interprtation.

Keeping the total between 10 and 17, there are several sets which multiplied together equal 120 such as (1, 2, 5, 12), (1, 3, 4, 10), (1, 3, 5, 6), (1, 4, 5, 6) and (2, 3, 4, 5). Only one set contains 2 as the fewest therefore knowing that the sister had more than one child would allow the math guy to determine the answer. However what sort of mathematician would know his friends house number but not how many children he had?

Simple,

From what he makes as a mathematician, he can only live in the street.

Wangito.

Remember the part about not enough children to make 2 ball teams? That limits the number sets to total no more than 17 which negates 1+2+5+12=20 and 1+3+4+10=18. Also, 1x3x5x6=90 not 120.

The mathematician does know the house number and the number of children his friend has.

My bad on the first two, (1, 2, 5, 12) and (1, 3, 4, 10) but the third was supposed to be (1, 3, 5, 8). Well that was my bad too but a different kind of bad.

How about 1+4+5+6? Product is 120. OK, with this hint you should be able to solve with logic.

1+4+5+6 was already stated in my 1st response (#9) as well as 2+3+4+5. My correction (#14) stated 1+3+5+8. With these 3 possibilities I think have already solved the problem.

Yes you have.

I didn't catch this the first time but if:

>The mathematician does know the house number and the number of children his friend has.<

then there is no reason to ask about the sister.

The reason the mathematician asked if the sister had more than 1 child was to be able to solve the problem. If the sister had only 1 child the mathematician would be unable to solve. See reply#18

If the only three possibilities are 1+4+5+6, 1+3+5+8 and 2+3+4+5 and the mathematician (per your response #13) knew how many children his friend had (5, 6 or 8), why did he need to know how many children the sister had? (or was he a lousy mathematician?)

Excellent!!!! I do not believe in the original question it was stated that the mathematician knew how many children his friend had. I added that later in a response and your logic proves that the question asked by the mathematician is unnecessary if the number of children his friend had was known.

In this case you are right. So the original question must state that the mathematician did not know how many children his friend had.

I bow to your superior logic and keen intelligence.

Logic not being one of my strong points (along with common sense), I thought I'd challenge myself and try to answer this.

I get 38 different combinations of children that satisfy the two conditions (4 different numbers whose sum equals 9, 10, 11, 12, 13, 14, 15, 16, or 17). Nobody said they were linear combo's...

We could assume the mathematician knows the friend's house number- being a number- but we could also notice that 120 is the only product of these 38 combinations that has either 1 or 2 as a possibility for the sister's spawn. Because the mathematician had to ask whether she had 1 or 2 kids, we know the house number must be 120.

There are three combinations that have 120 as a product:

1,3,5,8 (sum = 17)

1,4,5,6 (sum = 16)

2,3,4,5 (sum = 14)

Since the friend answered this question and the mathematician then knew the correct numbers, we know that the sister does not have only 1 kid. This would have required the mathematician to ask one more question to get the numbers.

Therefore, the house number is 120, the friend has 5 kids, his brothers have 3 and 4, and his sister has 2.

Jim

You underestimate yourself. Your answer and logic are absolutely correct. Congratulations!!!!