- 22 hours ago
- 4 min read
Howdy! It’s the Chess Friends!
Today we are going to share two of the coolest math problems in chess, The Eight Queens Puzzle and The Knight's Tour. We all love math, almost as much as we love chess, so these are particularly special.
The Eight Queens Puzzle
The goal of this puzzle is to place eight queens on the 8 x 8 chessboard so that none of them threaten one another, meaning that they are each on a different row, different column, and different diagonal.
This puzzle was created by German chess composer Max Freidrich William Bezzel in 1848, and there are now variations that extend this puzzle to smaller and larger board sizes, like place 7 queens on the 7 x 7 chess board, or 9 queens for 9 x 9 board. Believe it or not, there are 92 solutions to this 8 x 8 problem, and only one that is symmetrical. Can you find any? How about the symmetrical one?
We would like to show you some examples here, to set you on the right track. Here is a solution we came up with to the five queens puzzle on a 5 x 5 board.
Here is a solution we created on a 9 x 9 board with 9 queens!
Do you notice anything interesting about the queens? Many of them are a knights jump away from one another! Why do you think so? We think that if they’re a knights jump away from each other, they’re not touching and they’re on different ranks, files, and diagonals, which is the goal!
The Knight’s Tour
The Knight’s Tour is a puzzle. The goal is for a knight is to go to every square on a chessboard without repeating a square.
This problem was created around 800AD by Indian poet Rudrata. We have a painting of the Knight’s Tour in our living room, by local artist Jayashree Krishnan! In particular, there are two poems from the Paduka Sahasram, which is a collection of 1008 poems written in the 12th century by Vedanta Desikan. Note that the Sanskrit characters to start each move of the tour are painted on each square.
This problem becomes even more difficult if we want to do a closed Knight’s Tour meaning the Knight must return to its home square so if you want an even greater challenge, give it a go! Believe it or not, if you include transformations like reflections and rotations, there are 26,534,728,821,064 closed Knight’s Tours!
Extending this problem to boards of different sizes is a famous problem not only in math, but in computer science as well. We would love for you to play with it and try to solve the 8 x 8 case, that is move the knight to all 64 squares without repeating a square but we’ll give you a few tips here.
One neat trick to solving this problem is Warnsdorf’s rule, which says the knight should always move to the square with the least number of possible moves after that you haven't yet visited. Here’s an example:
Suppose the knight is on b4 as you can see above. There are six squares it can go to: a6, a2, c6, c2, d5, and d3. If it goes to c6, d5, or d3, it has 7 squares it could then go to without returning to b4. We can do better! If we go to c2, there are only five squares the knight can go without returning to b4. Better but not the best. How about a6? From a6 we can go to b8, c7 or c5, so only 3 options. Pretty good! What about a2? I think we have a winner! The only squares the knight can go from there are c3 and c1, so since there are only 2 options, we choose that as our next move. Note that this is an algorithm, or a method we can follow to get us to a solution. Sometimes the fun is in playing and experimenting yourself, but we wanted to share this in case you wanted a process to follow.
Here is a full solution to the Knight’s Tour on a 5 x 5 board:
The Magic Square Knight’s Tour
There is a special case of the Knight’s Tour where the numbered sequence of moves forms a Magic Square. A Magic Square is a square with distinct positive whole numbers on each square such that each row and each column has the same sum.
Here’s an example of one of ours from elementary school! Fun fact: The Man’s Halloween costume in 2nd grade was a knight on a Magic Square Tour!! Like most math problems, Magic Squares have extensions too, and one of those is where the diagonals also add up to the same number!
We’ll leave these here for now friends. We hope you learned a little bit and have some tools to experiment with these awesome chess math puzzles. Good luck! Feel free to share your solutions and thoughts in the comments! Do math! Play chess!
Three Cheers, Fellow Future Master Chess Friends!
The Man Benji, The Myth Sarang, and The Legend Vivi
- Jun 5
- 2 min read
Howdy! It's the Chess Friends!
Today we're going to play a game of Would you rather? with The Chess Friends! Remember The Man is Benji, The Myth is Sarang, and The Legend is Vivi. Let's dive in!
WOULD YOU RATHER...
Play White or Black?
Man: White Myth: White
Legend: Black
Play Blitz or Classical?
Man: Blitz
Myth: Classical
Legend: Blitz
Play Bughouse or Bullet?
Man: Bughouse
Myth: Bullet
Legend: Bullet
Play Over the Board (OTB) or Online?
Man: OTB
Myth: OTB
Legend: OTB
Play Magnus or Gukesh?
Man: Magnus
Myth: Magnus
Legend: Gukesh
Become a Chess Streamer or Chess Grandmaster?
Man: GM
Myth: Streamer
Legend: GM
Play chess or study chess?
Man: Play
Myth: Study
Legend: Play
Never run out of time or have infinite opening knowledge?
Man: Infinite opening knowledge
Myth: Infinite opening knowledge
Legend: Infinite opening knowledge
Play a tournament locally or travel to a tournament?
Man: Travel
Myth: Travel
Legend: Local
Get 3/6 playing up every round or 6/6 playing down every round?
Man: 6/6
Myth: 3/6
Legend: 3/6
Open e4 or d4?
Man: e4
Myth: e4
Legend: d4
Greek gift or Botez gambit?
Man: Greek gift
Myth: Greek gift
Legend: Botez gambit
Win a Middlegame or Endgame?
Man: Endgame
Myth: Endgame
Legend: Middlegame
Play a Gambit or No Gambit?
Man: No Gambit
Myth: No Gambit
Legend: Gambit
Play a morning round or evening round?
Man: Morning
Myth: Evening
Legend: Morning
Castle Kingside or Queenside?
Man: Queenside
Myth: Kingside
Legend: Kingside
Use Pawns or Pieces?
Man: Pieces
Myth: Pawns
Legend: Pawns
Play Kids or Adults?
Man: Adults
Myth: Adults
Legend: Adults
Attack or Defend?
Man: Attack
Myth: Attack
Legend: Attack
Play a brilliant move or have 99% accuracy?
Man: Brilliancy
Myth: 99%
Legend: Brilliancy
Play the Hippo or the Cow?
Man: Hippo
Myth: Hippo
Legend: Cow
Write about Chess or read about Chess?
Man: Read
Myth: Write
Legend: Write
How would you answer these questions? Let us know in the comments! Note that both is not an option nor is neither! It's tough! Good luck!
Three Cheers, Fellow Future Master Chess Friends!
The Man Benji, The Myth Sarang, and The Legend Vivi
- May 29
- 2 min read
Howdy! It's the Chess Friends!
When you start writing a book, it's going to be messy and that's a good thing! Today we'll share some of our brainstorming process and ideas that didn't quite make it. We started with lots of brainstorming sessions and came up with many ideas for questions our book would answer. Then to bring everything together, we discussed title ideas. Here are a few:
The Basic Chess Book for Kids
The Ultimate Guide to Chess Tournaments
The Q & A Chess Book
Kids Teach Kids Tournament Chess
How to Play Chess Tournaments: For Kids By Kids
Chess As We Know It
A Guide to Chess Tournaments for Beginners and Beyond
After looking at all the ideas, we found common themes and words and tried to combine them. Our working title for a few months was:
The Ultimate Guide to Tournament Chess:
Frequently Asked Questions and Stories by Kids
As we worked, particularly on cover ideas (stay tuned for the big cover reveal!!), the title felt like it was too long and unnecessarily complicated. We then decided on our current title:
Q & A Chess:
Tournament Edition
We really like this as it's short and sweet, highlights the format of the book, and gives us flexibility to make future projects under the heading Q & A Chess.
We initially wanted to make our book in a graphic novel style with lots of comics but ultimately decided that it would be a bit too challenging to share sufficient detail. That's when we decided to create our buddy Peshka, with speech bubbles, who you'll see throughout the book, offering advice and comic relief. Let's be honest, a little comic relief goes a long way in life!
Here's an example of one of our comic strip ideas:
We will write a blog post on the evolution of Peshka soon! Before we let you go today, we wanted to share a fun fact from this past week. We all played in the WA Open Chess Championships and something crazy happened in round 4...
The Man Benji got paired against The Myth Sarang! What are the odds?! In our book we discuss the question "Is it weird to play a friend?" and the answer is complicated. We both played very well and postgame analysis revealed impressive accuracies around 95 percent each. There were definitely many giggles! What can we say? We are chess friends first and competitors second. Can you guess the result?
Three Cheers, Fellow Future Master Chess Friends!
The Man Benji, The Myth Sarang, and The Legend Vivi