Losing my marbles: The Weekly Puzzle by Dilip D’Souza
My friends Janak and Kanak both love logic games. When they came to visit once, I gave each of them some marbles. I did this in a way that neither knew how many the other had (of course each did count their own stash), though I did tell them they had different numbers of marbles.
Then I asked: Which of you has fewer marbles?
This conversation ensued:
Janak: Dude, I have no idea which of us has fewer marbles!
Kanak: Nor do I, bro!
Janak: Gotta say, sadly, I still have no clue!
Kanak: Wait a minute! Now I know who has the smaller number!
Janak: Oh yeah? Well, I know both our counts now!
Question: How many marbles did each have?
Scroll down for the solution and answer.
With Janak’s first answer, we know he doesn’t have 1 marble — because if he did, he’d know he had the smaller number because there’s no number smaller than 1.
Kanak absorbs this, but still doesn’t have an answer. That must mean she doesn’t have 2 — for if she did, she’d know hers had to be the smaller number.
Now Janak absorbs this too, but he too still can’t answer. Thus he doesn’t have 3 marbles.
But now Kanak knows the answer — she has the smaller number, because she must have either 3 or 4. (If 4, that would be the smaller count because Janak doesn’t have 3).
And when Janak says he knows both counts, that must mean he has 4 (because we know he doesn’t have 3) and Kanak has 3. (If Janak has any count greater than 4, he wouldn’t know what Kanak’s count is — 3 or 4).
Thus: Kanak 3, Janak 4. And after handing them out, I’ve lost all my marbles.