How many children

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
Gold Member
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!

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

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.

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

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.

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wow that was great thinking!

amazing