I’m certainly no math whiz, but I do like puzzles.

I have the answer narrowed down to two possibilities. Is my reasoning correct? What am I figuring incorrectly that I can’t narrow it down to just one?

For those who still want to figure it out independently of my attempt, I will post my reasoning in a spoiler box:

[spoiler]OK… anyone who likes puzzles has seen other puzzles like the one they are trying to do, and this one is no exception. I’ve seen another puzzle where the product of something totaled an amount you are not told, but when the person in the story asked a follow-up question, was able to produce an answer, even though the reader was not told what that answer was. The trick was that the product could only be made up of a limited amount of factorials, and only one solution had (or didn’t have) a duplicate number in the factorials.

Applying the same logic here, we are told that the total number of children is less than two baseball teams; that is, the total number of children must be under 18: 17 or less. We are also told that each family has a different number of children, that is, no two have the same number. The smallest combinations of numbers that work would be 1, 2 3 and 4. That adds up to a total of 10. If the largest family was 6 children, followed by 5 then 4 then 3, that adds up to 18, which is too much. So the numbers must be less than that. The only numbers that are possible given these two limitations, then, are the following (with their products, which will be the next step):

6,5,4,2 = 240

6,5,4,1 = 120

6,5,3,2 = 180

6,5,3,1 = 90

6,5,2,1 = 60

6,4,3,2 = 144

6,4,3,1 = 72

6,4,2,1 = 48

6,3,2,1 = 36

5,4,3,2 = 120

5,4,3,1 = 60

5,4,2,1 = 40

5,3,2,1 = 30

4,3,2,1 = 24

Now, we are told that the product of the four numbers equal the house number (and we are not told what number that represents). But notice of all the products of the possible four numbers, only two sets have the same products, all others produce products that are different from all the others. If any of those were the correct numbers, the person in the story would know the answer right away (he has seen the house number, we are told). So it must be one of the two sets that produce duplicate products:

Both 6,5,4,1 and 5,4,3,2 have the same product of 120

Both 6,5,2,1 and 5,4,3,1 have the same product of 60.

Then we are told the person in the story had one last question: was the smallest family size 1 child? Although we are not told the answer, we know that provided the person in the story with enough information to deduce the correct answer. Of the two different possible sets, the second set both have 1 child, so the answer would not be helpful to narrowing down the two to one correct answer.

The other possible set is either 6,5,4,1 or 5,4,3,2. Knowing if the smallest family has one child would tell us which of the two is correct.

But as I don’t know the answer to that question, I cannot see how to narrow the two down to one myself.

Am I missing something simple? Am I completely off?[/spoiler]**Padeye**, on preview I see your posts. A spoiler box is easy, it’s just a tag before and after the spolier. the tag before is <spolier> (with the square brackets “[” instead of the “<”) and the end tag is </spoiler>