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Topic: What's the Scoop?
Message: Posted by: Scott Cram (Apr 11, 2004 04:09PM)
Here at Ma and Pa's Ice Cream Shoppe, a sign advertises the flavors along with a list of toppings available for each flavor, as shown below:

Available toppings for mocha: marshmallow or caramel
Available toppings for mint chocolate chip: marshmallow, hot fudge, or butterscotch
Available toppings for chocolate: marshamllow, peanut butter, or caramel
Available toppings for vanilla: hot fudge, peanut butter, or butterscotch
Available toppings for strawberry: marshmallow

Pa always takes the orders and scoops the ice cream; Ma adds the toppings and works the register. When I popped in for a snack recently, I decided to mix things up a bit, so I announced that I would whisper my topping selection to Pa and my flavor selection to Ma. After I did so, the proprietors looked at each other and had the following conversation:

Ma: I don't know what topping to give him.
Pa: I knew you didn't.
Ma: I didn't know that.
Pa: Now I know what to scoop.
Ma: Now I know what topping to put on.

They made me the sundae I'd ordered and sent me on my way. What did I order?
Message: Posted by: Samuel Catoe (Apr 11, 2004 05:08PM)
You have me stumped.
Message: Posted by: pxs (Apr 12, 2004 02:51AM)
I would say Chocolate and Peanut Butter (I think)
(Nice puzzle by the way - Ma and Pa sure are logical!)
Message: Posted by: MacGyver (Apr 12, 2004 08:52PM)
Ok:

Available toppings for mocha: M or caramel
Available toppings for mint choco late chip: M, hot fudge, or butterscotch
Available toppings for chocolate: M or peanut butter, or caramel


Ma: I don't know what topping to give him.
-This means that it couldn't have been strawberry because then Ma would have known it was marshmello.

Pa: I knew you didn't.
-This means Pa knew she didn't have Strawberry, which means he wasn't told marshmello or he would have been unsure if she knew or not.

Ma: I didn't know that.
-That means that Ma didn't know whether Pa was told marshmello or not, which excludes vanilla because it doesn't have marshemello.

Pa: Now I know what to scoop.
- He couldn't have Caramel because that would leave mocha and chocolate, and he wouldn't know which to scoop. So the topping either had to be Hot fudge or butterscotch(indicating he had mint chocolate chip) or peanut butter(indicating he had chocolate).


Ma: Now I know what topping to put on.
- This means it must be Peanut butter, because if she was sure, then there must have been only one topping left(peanut butter), so that means that for it to be mint chocolate chip, she would have had to have been unsure about the topping. Upon hearing that he was set with the type of ice cream,


So my answer is Chocolate w/ Peanut butter.

However, the answer could have also been mint choc. chip with either hot fudge or butterscotch, but then the last two lines would have been different.

I wondering how they would have handled it had you chosen something like the mint choc. chip w/ butterscotch, because the method that they used to find eachother's object wouldn't have worked because if he had said "I know what to scoop" and it was mint chocolate, she still would have no idea which topping to use.
Message: Posted by: Scott Cram (Apr 13, 2004 10:26AM)
Congrats, pxs and MacGyver, you're correct!

How would I handle mint chocolate chip with butterscotch? Easy. I walk in and say, "I want mint chocolate chip with butterscotch", instead of whispering it to them.
;)