A game is considered to be “solved” when all of the possible moves have been mapped out in a mathematical tree and thus the perfect set of moves can be determined regardless of an opponent’s play.

Tic-Tac-Toe is a pretty easy one. You solved this as a kid. There are three opening moves – corner, edge, center. And then you work from there.

Connect Four was solved in 1988. That’s because those new-fangled computer thingies were starting to get some real power behind them. If you want to play Connect Four against the best opponent you’ve ever played in your life, check out the applet on John’s Connect Four Playground which is programmed to play flawlessly, based on a database of pre-determined best moves. But if you go first, and play just as flawlessly, you can beat it.

Checkers was solved this past April by researchers from the University of Alberta. You can play against Chinook, which will play flawlessly, but the best you can hope for is a draw. It doesn’t matter how amazingly good you are at checkers. You will never win. For me, there’s something a little disturbing about that.

Could chess be next? There are an incredibly large number of possible games, but it must be finite. And if it’s finite, then the tree must conceptually exist even if nobody has been able to come close to mapping it yet. Some see chess playing ability as intutive and creative, and not merely a number cruching process. But if number crunching continues to get better, it might evolve to the point where we get a chess-playing program as unbeatable as Chinook.

To be clear, we’re not talking about a really, really good chess-playing program. We have that now. We’re talking about a program that can access an exhaustive database of pre-determined best moves in order to ensure the most favorable outcome possible.

What do you think?

Will computers ever solve chess?

Last week’s Conundrum about kings named Henry reminded me of a Shakespeare final I gave about five years ago. This was for an advanced graduate course on Shakespeare, and I actually decided to give the final exam as a takehome. What’s more, the first five questions were True or False. Surprisingly, only two students got all five questions right. Sounds like quite a Conundrum to me…

TRUE or FALSE?

1. Twelfth Night is named after a holiday in December.

2. Gloucester (in King Lear) has two sons; the bastard one is named Edmund.

3. Katherine of Valois was wife to Henry V, mother to Henry VI, and grandmother to Henry VII.

4. Based on evidence in Hamlet, it is reasonable to assume that Shakespeare may have read at least some of the writings of Sigmund Freud.

5. The title of The Merchant of Venice refers to a Jewish merchant named Shylock.

I should point out that the five questions combined were ten percent of an exam that was ten percent of the final grade, so these questions alone were not enough to affect anyone’s final grade. I don’t believe in trying to trick students, but I felt that a takehome exam deserved a little extra bite. The rest of the exam was short answer and essay and was very straightforward.

Can anyone answer all five questions correctly?

England has had eight kings named Henry, all before Shakespeare was born.

How many of the eight appear as characters in Shakespeare’s 37 canonical plays?

For your answer to be valid, please list each such Henry, and at least one play in which he appears. It is not necessary to list all of the plays in which each Henry appears, but maybe we can do that after the Conundrum is solved.

Note: The Henry does not need to have been king at the time – nor, for that matter, called Henry.

UPDATE: Question answered by K-Lyn. See comments for answer.

Four poker friends played a hand of five-card stud. Each player was dealt one hole card face down, and then four additional cards face up. The cards were dealt, as in standard poker, one at a time around the table, from one regular poker deck. However, instead of betting each round, they decided to deal all twenty cards out in the beginning, and let winner take all!

1. As it turned out, any two consecutive cards dealt in this hand were either different color cards of the same rank or were consecutive ranks of the same suit, considering Aces as high cards only.

2. At least three of the four hole cards were Queens.

3. The last card dealt was a Heart.

4. At least one player was dealt more than one Ten. Nobody was ever dealt a Nine.

5. No Diamond was ever dealt immediately before or after a Spade.

6. Ron was dealt no Clubs, Lenny was dealt no Kings, Nick was dealt at least one Jack, and Frank’s hole card was a Spade.

Who won, and with what hand?

UPDATE: Puzzle solved by ArtVark. See comments for answer.

In a normal “Pic Tac Toe” puzzle, there are nine pictures in a 3×3 grid, like Tic-Tac-Toe. In each of the three rows, three columns, and two diagonals, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

In this “Pic Tac Toe” puzzle, however, there are twenty-seven pictures in a 3×3x3 grid, like a Rubik’s Cube. In each of the nine rows, nine columns, nine pillars, eighteen lateral diagonals, and four cross-cube diagonals, there is a common theme that unites the three pictures. The challenge is to find the forty-nine themes.

Imagine stacking the three levels below on top of one another. For reference, and notation guidelines, check out my last 3D Pic Tac Toe, including the comments. The rules here are identical to that puzzle.

You can click on each image to see a larger version:

Top Level – Level A

Middle Level – Level B

Bottom Level – Level C

Please post whatever you come up with in the comments section.

Enjoy!

UPDATE: Correct themes provided by Neel Mehta (35). Alternate themes suggested by Neel Mehta (6) and K-Lyn (1). See comments for discussion, or click here to skip right to the answers.

You may want to use a map for this one…

Imagine the 2008 Republican primaries are over, and only four candidates won any states. (DC, which is not a state, went to Ron Paul.)

1. Mitt Romney won more states than any other candidate.

2. Rudy Giuliani’s states included Massachusetts and Washington.

3. John McCain won all of the states beginning with one particular letter, and only those states.

4. Fred Thompson’s states included New Mexico.

5. Strangely enough, no two bordering states went for the same candidate. (Four Corners does not count as a border.)

Who won in Michigan? How do you know?

UPDATE: Puzzle solved by David. See comments for solution.

In a normal “Pic Tac Toe” puzzle, there are nine pictures in a 3×3 grid, like Tic-Tac-Toe. In each of the three rows, three columns, and two diagonals, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

In this “Pic Tac Toe” puzzle, however, there are twenty-seven pictures in a 3×3x3 grid, like a Rubik’s Cube. In each of the nine rows, nine columns, nine pillars, eighteen lateral diagonals, and four cross-cube diagonals, there is a common theme that unites the three pictures. The challenge is to find the forty-nine themes.

Oh, yeah. I went there.

You can click on each image to see a larger version:

Top Level

Middle Level

Bottom Level

Please post whatever you come up with in the comments section.

Enjoy!

UPDATE: Correct themes provided by Neel Mehta (30). Alternate themes suggested by Neel Mehta (5). See comments for all answers.

In a “Pic Tac Toe” puzzle, there are nine pictures in a three-by-three grid, like Tic-Tac-Toe. In each row, column, and diagonal, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

You can click on each image to see a larger version:

Please post whatever you come up with in the comments section.

Enjoy!

UPDATE: Correct themes provided by Annalisa (7) and Neel Mehta (1). See comments for all answers.

In a “Pic Tac Toe” puzzle, there are nine pictures in a three-by-three grid, like Tic-Tac-Toe. In each row, column, and diagonal, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

You can click on each image to see a larger version:

NOTE: Pictures 4 and 6 carry a watermark from iStockphoto. This is not part of the puzzle.

Please post whatever you come up with in the comments section.

Enjoy!

UPDATE: Correct themes provided by Neel Mehta (1) and Annalisa (6). See comments for all answers.

In a “Pic Tac Toe” puzzle, there are nine pictures in a three-by-three grid, like Tic-Tac-Toe. In each row, column, and diagonal, there is a common theme that unites the three pictures. The challenge is to find the eight themes.

You can click on each image to see a larger version:

Please post whatever you come up with in the comments section.

Enjoy!

UPDATE: Correct themes provided by Neel Mehta (8). Alternate themes suggested by Neel Mehta (2). See comments for all answers.