Particularly Clever Puzzlers

Some puzzlers are particularly clever. Some, not so much. The really good ones are very simple to state, but not so simple to solve

The Monty Hall puzzler is a good example of a clever puzzler: You are presented with three doors, behind one of the doors is a car you can keep if you happen to choose that door. You choose a door at random. Then one of the other two doors is opened for you, showing it doesn’t contain a car. You are given a choice to keep your current door, or switch to the other door. Which should you do?

Another clever one, on Car Talk podcast not too long ago: You are presented with three opaque bags, each containing marbles. You can’t see inside the bags. Each bag is marked with a label, white, black, or mixed (half black/half white). None of the labels are on the correct bag. Your goal is to place the all three labels on their correct bag. You can look in the bags at as many marbles as you like, from any or all of the bags. What’s the best strategy to determine where the labels go by looking at as few marbles as possible?

You are of course welcome to chime in with answers. But the reason I’m posting, can you folks think of any other really clever puzzlers like these two?

I don’t like puzzles. I like answers instead.

On the first one, I’d just keep the same door. Gotta 50 50 chance. Of course I always suspect fraud with all of the doors empty.

On the marbles, seems to me you just check two bags to find any black or white ones. But I wouldn’t pick up individual marbles, I’d just stick my hand in to stir them up. But I don’t like following rules either.

Do you remember the old TV Game Show, “Let’s Make a Deal” with Monty Hall? On one of the shows a contestant chose a door that turned out to be a “Zonk” and it contained a small oil derrick or something similar. Contestants are not suppose to get to keep the Zonk even if they wanted to since they are actually expensive movie props in many cases and are suppose to be awarded a small cash prize. The contestant that won that Zonk was not going to go along with that and they sued. That piece of equipment was worth a lot more than the car he did not win and after it was all said and done he got that new car, but with the cash settlement…


Incorrect decision. This is a classic mind teaser debated for centuries. The correct answer is to chose the other door for reasons I won’t go into. Wikipedia actually has a good explanation of why it is better to chose the other door.

You better check that part again,

I prefer puzzlers that are automotive not math oriented.

I alway read the column that I think was titled “Last Chance Garage” in Mechanix Illustrated. Each month Gus, the garage owner, was presented with a problem, then solved it.

The one problem with the ‘Monty Hall’ puzzler is that it ignores Monty’s ability to decide whether or not to show one of the two curtains. What if Monty only did that when the contestant had the winning curtain?

That puzzler should include something like ‘Monty always shows one of the curtains’ to eliminate this problem.

I was an avid follower of that column, and it taught me quite a few things about car repair before I was old enough to drive.

The most memorable one had to do with the woman whose engine ran badly after it had warmed-up, had poor power output, and consumed a huge amount of gas, but always performed flawlessly when Gus test-drove it. Gus was stumped until he observed that the woman pulled-out the choke control and hung her handbag on it.

Once Gus explained how to use the choke correctly, and explained why this wasn’t a good place to hang her handbag, the woman’s car problem disappeared.

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The last car I had with a manual choke was my 59 vw. I’m sure kids have no idea what that is. Now my lawn mower has a manual choke yet but my wife never uses it and I don’t have a purse.

No doubt that people younger than… I guess… 50 or so have no idea what a manual choke is. And, some of those same folks might not even know how to set an automatic choke. Conversely, I know a guy who bought a Scion about 8 years ago, and I had to explain to him that he didn’t need to “set the choke”. His previous car was a '59 Dodge.

The car in question, in Gus’s Model Garage, was something from the early '50s.

Correct. Usually when this particular puzzler is posed, it’s not stated that the host knows which door contains the car, and always opens the door that doesn’t. This fact is what changes the optimal strategy. But we’re always being presented with decisions where some of the facts are well known to the presenter, but aren’t clearly stated to us. Just look at the small print on your next bank account statement …lol…

I don’t understand your point. The puzzler objective is to determine the label positions by looking at as few marbles as possible. Doesn’t mean you can’t look at as many as you want in as many bags as you want, but that method may not be (i.e. isn’t) the optimal strategy. If I’m missing something, suggest to clarify.

As quoted by VDCdriver’s in posting, my 1954 Dodge Meadowbrook had “Two Handbags Holders…” My Dodge had both a Choke and a Throttle Control. The Choke only “choked” the Carb and the Throttle raised the RPMs…

I grew up in UpState NY, where snow fell in “Feet” rather than “Inches” and and my '54 had a 6-Volt system so I mounted a 12-Volt battery behind the Grill, in front of the radiator for those cold morning starts… That car usually only need a touch of choke to start…

I think one of the reasons CarTalk was & continues in “Best of” format to be very popular is b/c of the bizarre car-related puzzles the callers present to the two hosts. "My car won’t start, but only when it is in the vicinity of a particular ATM. Other ATM’s, no problem. I told this to my friend owning the same make/model. She said her car won’t start when her car is in the vicinity of another ATM. "

What? …lol …

You’d think Albert Einstein in particular would have enjoyed math related puzzles. But this was said to be his favorite:

Albert Einstein … claimed that 98% of the people are incapable of solving it. (Note: This one doesn’t meet the “simple to state” criteria for a really clever puzzle. But it is still fun to try to solve. )

Let us assume that there are five houses of different colors next to each other on the same road. In each house lives a man of a different nationality. Every man has his favorite drink, his favorite brand of cigarettes, and keeps pets of a particular kind.

  1. The Englishman lives in the red house.
  2. The Swede keeps dogs.
  3. The Dane drinks tea.
  4. The green house is just to the left of the white one.
  5. The owner of the green house drinks coffee.
  6. The Pall Mall smoker keeps birds.
  7. The owner of the yellow house smokes Dunhills.
  8. The man in the center house drinks milk.
  9. The Norwegian lives in the first house.
  10. The Blend smoker has a neighbor who keeps cats.
  11. The man who smokes Blue Masters drinks bier.
  12. The man who keeps horses lives next to the Dunhill smoker.
  13. The German smokes Prince.
  14. The Norwegian lives next to the blue house.
  15. The Blend smoker has a neighbor who drinks water.
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I don’t care if I’m a 98%er. I’m not even going to try. Y nephew is an engineer and when faced with a problem he will start out with “solve for”. I guess they teach that in engineering school. Business people would just go knock on the doors and start a conversation. Might be able to sell something or get an idea for a product.

This afternoon I solved for how to cut a slot in a rocker patch panel when your drill bits are round. That’s my speed.

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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.

That seems like a valid puzzler. Good for you for solving it.

One rumor among scientists, probably not true, is that Einstein purposely gave this puzzle to students to solve who wanted him to be their thesis advisor, in an attempt to get them to ask somebody else, not bother him … lol …

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That’s one version of a set of possible restrictions a person could be presented with for this puzzle. If your point is that those are the particular restrictions as stated in the Car Talk puzzler, ok, but does it change the optimal solution?

That is the restrictions of the puzzler as posted on Car Talk Puzzler.

The puzzle can be solved by opening only 1 bag and pulling only 1 marble out.

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Heh heh. On a long hot drive through Wyoming. My dad and I were taking turns trying to put one of those wooden puzzles together. I figured it out but he was still working on it. Then the directions flew out the window and I heard some words that made my little ears burn.