Feb 18, 2023
It is time for the new puzzler. This one isn't really automotive in nature. But we will set it in the back seat of a car, so that way, it will be kind of automotive. Quasi-automotive, if you will.
This is a cute little puzzler, I think. A wonderful little riddle, kind of.
So, you're in the back seat and have three little felt drawstring bags. In each of these bags, you have 10 marbles. 10 marbles total, in each bag.
One bag is filled with 10 black marbles.
One bag is filled with 10 white marbles.
And the last bag is filled with half and half, 5 black and 5 white.
Each bag has a little label on it. However, the labels are incorrect. None of them are right.
So, you are allowed to reach your hand into a bag, but you are not allowed to look at the colors of the marbles in the bags. You are allowed to reach in and remove one marble from a bag, and then you can look at that marble. But then you have to return that marble back to its bag without looking at the rest of them. You can only have one marble out of a bag at a time. So, you take one out, look at it, then return it. You are then allowed to pull a marble from another bag, look at it, and then return it. And so on and so on.
So, here is the question.
How many times do you have to do this to identify each bag? In other words, how many peeks do you get of one marble from one bag at a time, before you can clearly identify which bag is the all black bag, which is the all white and which is the mixed bag?
Good luck my friends.
It is time for the answer to our latest quasi-automotive puzzler.
This one was cute. About bags of marbles. Three different bags, with 10 marbles each. One bag of all black marbles. One of all white marbles. One of mixed, half and half, 5 of each color. 30 marbles total.
Each little bag has a label on it, but the labels are wrong.
Your job, should you choose to accept it, is to determine which label goes where. But you can't look inside the bags. You can only put your hand in and pull out one marble at a time. You're allowed to look at it and then put it back.
So, with all these rules in place, how many times would you have to reach into the bags to determine which bag is which? In other words, how many peeks do you get of one marble from one bag at a time, before you can clearly identify which bag is the all white bag, which is the all black and which is the mixed bag?
Here's your answer.
You would reach into the bag labeled mixed black and white marbles. And you pull out a marble from that bag. So, you know that since they are labeled wrong, you know that bag is not the mixed bag with black and white marbles. So it has to be filled with either solid white or solid black. So by pulling out one marble from that bag and looking at it, you know the color of that bag, right then and there. So, if you pull a marble from that bag and it is white, then you know this bag should be labeled as the white marble bag. So you put the first mix label on the other bag which you just pulled the white label from. Now, you have the white marble bag labeled correctly.
Now, you are going to switch the labels on the other two bags. Because we know, with our rules, that all the bag are labeled incorrectly. So, after correctly labeling the all white bag, you know that the other two are still wrong. So by switching them, you will automatically be labeling them correctly.
So, the answer was, you only have to pull one marble from the mixed bag to be able to tell what all three are and label them correctly.
And you're done. Isn't that elegant?
