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

- Can You Solve This Extremely Difficult
*Star Trek*Puzzle? - You Either Solve This Riddle, Or You Die
- Can You Solve 'The Hardest Logic Puzzle In the World'?
- You'll Need All 3 Clues To Solve This Puzzle
- Think You Know The Solution To This Classic Riddle? Think Again.
- 100 Lives Are On The Line In This Week's Puzzle. How Many Can You Save?
- Can You Figure Out This Parking Lot's Numbering System?
- To Solve This Riddle, Look To Your Family
- Solving This Puzzle Will Help You Grasp The True Nature Of Puzzles
- Can You Guess The Next Number In This Sequence?

## DISCUSSION

I believe I have a method that accomplishes the task in a maximum of five turns, with the possibility of accomplishing it in one, two, three or four if chance is on my side.

Go get your glasses. It's much easier that way.

1) After the first spin, grab either of the diagonal pairs, and flip them both Up. If the bell doesn't ring, you know the other diagonal pair is either Up/Down or Down/Down

2a) After the second spin, grab a set of diagonal pairs. If they are Up/Down or Down/Down, you know they are not the pair you originally handled so you flip them both UP and the bell rings/

2b) If you happen to grab the pair you did originally handle, flip them Down/Down. If the bells doesn't ring, you can conclude that the pair you haven't yet handled is Up/Down and that you have 3 Downs and 1 Up.

3a) After the third spin, grab any diagonal pair. If they are Up/Down, flip them both Down and the bell will ring.

3b) If the pair you grab is Down/Down, flip one of them Up. There will now be two adjacent Ups and two adjacent Downs.

4a) After the fourth spin, grab two adjacent cups. If they are both Up, flip them both Down and the bell will ring.

4b) If they are both Down, flip them both Up and the bell will ring.

4b) If they are Up/Down, reverse the orientation of both of them. You will now have a pair of diagonal Ups, and a pair of diagonal Downs.

5) After the fifth spin, grab any diagonal pair and reverse the orientation of both. The bell will ring.