JACK'S KIDS
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John: so Jack, how many kids you got now?
Jack: less than 5
John: well...how many?
Jack: figure it out; the product of their ages equals twice the sum.
John: that's nice; but not enough info.
Jack: my wife gave birth a year ago.
John: still not enough.
Jack: the age of my oldest is the same as the number on this door.
John: hmmm...that helps...still not enough.
Jack: the two in the middle...
John: stop there! I know how many kids you have, and also their ages...
Can you figure it out also??
You do need that clue for your answer.
> Jack: the age of my oldest is the same as the number on this door.
> John: hmmm...that helps...still not enough.
Seeing that number has helped John, so has eliminated some possibilities.
Go here to get an idea of what I mean:
Puzzle - Ages of Kids
Well, since no one seems interested in this famous(!) puzzle of mine,
here's the solution.
From the 1st 2 clues (less than 5, twice sum = product), John got these as possibilities:
3 6
4 4
1 3 8
1 4 5
2 2 4
1 1 4 6
1 2 2 5
1 2 3 3
2 2 2 2
The next clue (my wife gave birth a year ago) forced youngest = 1, so these left:
1 3 8
1 4 5
1 1 4 6
1 2 2 5
1 2 3 3
The next clue (the age of my oldest is the same as the number on this door)
means the number on door was 5, since John still couldn't tell; leaving;
145
1225
So last clue (the two in the middle) meant 1225 (145 only has 1 number in the middle)
No you didn't...you think you did
Before the door number clue, we're at:
1 3 8
1 4 5
1 1 4 6
1 2 2 5
1 2 3 3
If you jump the door clue and go to "2 in the middle", then you're left with:
1 1 4 6
1 2 2 5
1 2 3 3
Those 3 cases have 2 in the middle, right?
The door clue is a MUST, to eliminate 1 1 4 6 and 1 2 3 3; get it?
Anybody in the house care to bet?
No - if I told you I've four kids, and mentioned something about the 'two in the middle', then the two youngest or two oldest aren't going to be the same age.
Assuming, of course that a) 'middle' is referring to age and b) that 1 year and 1 month is the same as 1 year and 10 months are both 1 year.
GOOD point! Thanks.
Only thing is:
"if I told you I've four kids, and mentioned something about the 'two in the middle'
then the two youngest or two oldest aren't going to be the same age."
Doing this means you are "changing" the puzzle; per the puzzle, before you
told me this, you would have given me the door clue, which I would have used.
Anyhoo, thanks for your observation: I'll change my wording to eliminate this possibility.
No, it just means I've eliminated the superfluous piece of info you were including.
But yes, I see where it fits into your 'telling', as it were, of the problem.
I'm sure there are many cases where the door is a useful piece of information though. It's an interesting idea. Thanks.