Can You Solve This Puzzle Blindfolded?

This puzzle would be a lot easier without the blindfold. Are you up for the challenge?

Sunday Puzzle #17: The Four-Glasses Puzzle

Four pint glasses are placed on the corners of a square Lazy Susan. Some of the glasses are upright (up) and some upside-down (down). You are blindfolded and seated before the Lazy Susan. Your task is to re-arrange the glasses such that they are either all up or all down. Either arrangement is acceptable. If, at any point in the task, the four glasses are rearranged to be all up or all down, a bell will ring, signaling your successful completion of the task.


There is, of course, a protocol to all this. The glasses may be inspected and re-arranged in turns, according to the following rules:

1. Any two glasses may be inspected in a given turn. After feeling their orientation, you are permitted to reverse the orientation of either, neither, or both glasses.

2. After each turn, the Lazy Susan will be rotated through a random angle equal to some integer multiple of 90°.

To complete the task, you must devise a method which allows you to ensure that all glasses have the same orientation (either up or down) in a finite number of turns. Your method must not depend on luck.


We'll be back next week with the solution – and a new puzzle! Got a great brainteaser, original or otherwise, that you'd like to see featured? E-mail me with your recommendations. (We welcome any and all submissions, but we're particularly interested in your picks for the most challenging Car Talk Puzzlers of all time – see the"Car Talk Puzzler Recommendations" section, below). As always, be sure to include "Sunday Puzzle" in the subject line!


Art by Tara Jacoby

UPDATE: The solution to The Four Glasses Puzzle has been posted.

SOLUTION To Sunday Puzzle #16: 3 Boxes, 2 Lies

Last week, I presented you with one of Car Talk's self-proclaimed "toughest" Puzzlers and asked you to deduce which of three boxes contained a picture.


I received more than 150 correct solutions via e-mail this week (more than any week in the history of the Sunday Puzzle series!), but the first to provide a clear, well-articulated solution was Edward Kim. He even included a diagram:


"The picture," he writes, "is in the silver box. It's the only scenario in which only one of the inscriptions is true."

I selected this puzzle because it lent itself to a very systematic approach, but was just complex enough to lead you down the wrong path, if you weren't careful. The number of incorrect responses I received to last week's puzzle is a testament to the fact that what seems easy to one person is not always immediately obvious someone else (though I will admit that I found this puzzle to be the least challenging entry in Car Talk's collection of its "Toughest" Puzzlers).


Car Talk Puzzler Recommendations

Many of you stated that you found last week's puzzle easier to solve than many of Car Talk's usual Puzzlers. If this was your experience, I invite you to submit some examples of what YOU believe to be Car Talk's most challenging riddles. To submit your picks, drop me an e-mail and pose the riddle(s) you think deserve to be mentioned in Car Talk's roundup of Tough Puzzlers. I only ask that you not suggest any Puzzler currently listed in the show's collection, so head here first to check the (very short) list as it exists today.


Previous Weeks' Puzzles


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