I’ve written a few chess puzzles that are highly inspired by “The Chess Mysteries of Sherlock Holmes” by Raymond Smullyan. They are what’s known as “retrograde analysis” puzzles. By looking at the present, you can determine many things about the past. Unlike “mate in seven moves” puzzles, you do not need to be good at chess to work these out, you only have to be good at logic (and have a grasp of the rules of chess). Throughout these puzzles, it must be assumed that the players followed the rules of chess. Nothing else needs to be known.
By looking at the chessboard above, can you tell me on what square was the white queen captured? You can try it yourself, or you can keep reading and I’ll walk you through it.
Black is missing one piece, which means it must have been captured by the pawn on c3. White is missing three pieces, two of which were captured by the pawns on e6 and f6. In order for the black bishop to have been captured on c3, it must have first gotten to c3, which it couldn’t have done until the pawn moved to f6, capturing a white piece. The only white piece that could have been captured on f6 is the knight because it can jump over the wall of pawns (the white pawn didn’t move to take the black bishop until after the black pawn took a piece, so the white bishop and queen were still trapped). So, we know the white knight was taken on f6, and we know the black bishop was taken on c3. The black pawn on e6 took something, either the queen or the bishop. However, it couldn’t have taken the bishop because it’s a dark-squared bishop. Therefore, the white queen was captured on e6. Ta da!
Looking at the chessboard above, can white castle? Remember, a player can only castle if the rook and king have not yet moved, and the king cannot move through check. I’ll leave the answer as an exercise for the reader
As crazy as it may sound, the above puzzle is one of the things I’m most proud of in my entire life. What piece does not belong on the board? (For this riddle, assume one of the players cheated and just placed one of his captured pieces back on the board). This is a mind-numbingly difficult puzzle to solve. I put the answer in the form of a story which you can read below. I really can’t believe I came up with this, and again, I’m so very proud of it.
Facebook Ruby Scramble (Boggle) Solver
I wrote a Ruby program to play Scramble for me on Facebook. It has never lost (obviously). It’s 80 lines of code and uses yawl (yet another word list) for the dictionary and Appscript to send the keystrokes. Some people think I’m a “cheater”, but it’s just as impressive to program a computer to solve something as it is to solve it yourself.
How To Solve A Rubik’s Cube (No Memorization)
Like everybody else, I first solved a Rubik’s cube by following instructions like a robot. Eventually that got boring and I decided to solve it for real. This video explains the method I finally came up with to solve a Rubik’s cube without relying on any pre-memorized sequences of moves.
This doesn’t really count as a puzzle, but it’s damn awesome. My mom bought it for me for Christmas from the Museum of Modern Art. Read more here.
This is a fascinating game, and you can read more about it on Wikipedia. The idea is not to be the one stuck eating the poison apple. I used Ruby to program the computer to play flawlessly, but it also goes second and the second person always loses assuming that the first person plays perfectly, so I wish you luck!
This type of game is called “determinalistic” because the outcome is known beforehand assuming that each player plays correctly. There is quite a fascinating proof that the first player always wins called the “strategy stealing argument”. The thing is, any move the second player could play on his first move could have been played by the first player. Therefore, if there is a move that wins for the second player, the first player could play that move first. Thus, the second player must not have a winning strategy because the first player would steal it.
The Greatest Logic Puzzle Ever Written: The Broken Truth Machine by Raymond Smullyan
It’s from Raymond Smullyan’s book The Lady or the Tiger and in my opinion it is the best logic puzzle ever written.
You want to buy a truth machine. They are machines that have two lights, red and green, and truthfully answer any yes or no question. The truth machine store has three machines in stock. Unfortunately, the owner doesn’t know which light means yes and which light means no (and it could be different for different machines). In other words, green doesn’t necessarily mean yes. Also, one of the three machines is totally broken and flashes red or green in response to a question completely at random. You do not know which machine is which, obviously.
Assuming you don’t want to buy the broken machine, what is a single yes or no question that you can ask to a single machine that will allow you to determine which is a good machine to buy?
Please use rot13 to encode your answers so as not to ruin the puzzle for anybody else.