The Battle I am Losing

I want the world to be a better place. My contribution is teaching people to think. People who think make better decisions, whether they want to buy a house or vote for a president.

When I started my blog, I posted a lot of puzzles. I was passionate about not posting solutions. I do want people to think, not just consume puzzles. Regrettably, I feel a great push to post solutions. My readers ask about the answers, because they are accustomed to the other websites providing them.

I remember I once bought a metal brainteaser that needed untangling. The solution wasn’t included. Instead, there was a postcard that I needed to sign and send to get a solution. The text that needed my signature was, “I am an idiot. I can’t solve this puzzle.” I struggled with the puzzle for a while, but there was no way I would have signed such a postcard, so I solved it. In a long run I am glad that the brainteaser didn’t provide a solution.

That was a long time ago. Now I can just go on YouTube, where people post solutions to all possible puzzles.

I am not the only one who tries to encourage people to solve puzzles for themselves. Many Internet puzzle pages do not have solutions on the same page as the puzzle. They have a link to a solution. Although it is easy to access the solution, this separation between the puzzle and its solution is an encouragement to think first.

But the times are changing. My biggest newest disappointment is TED-Ed. They have videos with all my favorite puzzles, where you do not need to click to get to the solution. You need to click to STOP the solution from being fed to you. Their video Can you solve the prisoner hat riddle? uses my favorite hat puzzle. (To my knowledge, this puzzle first appeared at the 23-rd All-Russian Mathematical Olympiad in 1997.) Here is the standard version that I like:

A sultan decides to give 100 of his sages a test. He has the sages stand in line, one behind the other, so that the last person in line can see everyone else. The sultan puts either a black or a white hat on each sage. The sages can only see the colors of the hats on all the people in front of them. Then, in any order they want, each sage guesses the color of the hat on his own head. Each hears all previously made guesses, but other than that, the sages cannot speak. Each person who guesses the color wrong will have his head chopped off. The ones who guess correctly go free. The rules of the test are given to them one day before the test, at which point they have a chance to agree on a strategy that will minimize the number of people who die during this test. What should that strategy be?

The video is beautifully done, but sadly the puzzle is dumbed down in two ways. First, they explicitly say that it is possible for all but one person to guess the color and second, that people should start talking from the back of the line. I remember in the past I would give this puzzle to my students and they would initially estimate that half of the people would die. Their eyes would light up when they realized that it’s possible to save way more than half the people. They have another aha! moment when they discover that the sages should start talking from the back to the front. This way each person sees or hears everyone else before announcing their own color. Finally, my students would think about parity, and voilà, they would solve the puzzle.

In the simplified adapted video, there are no longer any discoveries. There is no joy. People consume the solution, without realizing why this puzzle is beautiful and counterintuitive.

Nowadays, I come to class and give a puzzle, but everyone has already heard the puzzle with its solution. How can I train my students to think?


One Comment

  1. Georgiy Kuznetsov:

    Two weeks ago I came across this post and realized that I had a new kind of puzzles. I just did not think in this direction. So I tried to post a comment, but the script was broken. I wrote to the blogger couple times, but the email account appeared to be disconnected either.

    Several days ago I posted the link to few demo puzzles on This group is not very active, some members expressed interest, nobody could solve anything this far. Today I found the commenting script working and went on to post this.

    Now, since I did it on Reddit, may I quote my posting? Thank you for your kind permission.

    Disclaimer: I neither sell anything, nor profit from any sales. I have no products or services to offer. I made some demos and prototypes, and I am seeking feedback. My software is 100% my JavaScript, no third party scripting, no ads, no user information collected and no money making by any mean.

    I think came across an entirely new kind of puzzles. I am not in this business, so I decided to bring it to your attention.

    I created a computer toy, which was supposed to be a construction set for temporospatial patterns. Those are the patterns unfolding and repeating in time.

    The toy (named [FIREPEGS]( was very simple, and I thought it would be easy. Soon I realized it could be a puzzle. I could show a pattern and challenge another user to produce it.

    Did you think of a jigsaw puzzle? There is some similarity indeed. The difference is, in FIREPEGS the elements act simultaneously according to the rules, and the image changes. To solve a FIREPEGS puzzle, one has to figure out what causes what, where and then.

    The toy was made for children. The idea was that playing with space, time and causality would prepare them for engineering and science. Hence, I was looking for the easy challenges pushing aside the hard-to-solve ones.

    Guess, the hard-to-solve challenges has reached the critical mass because recently I made a e-booklet introducing few of them. It is available at [](


    The biggest reason I did not do it earlier was what the toy takes some learning. For a beginner, it’s probably on par with checkers. I thought, nobody would want to learn it to solve a puzzle or two. Now even I collected enough of them, and I am sure you will find more.

    The booklet tells what to see and what to do. If you prefer me to introduce the toy right here – OK, FIREPEGS is a community of cellular automata on a regular grid. If you happened to play with Conway’s Life ( you will understand FIREPEGS quickly. Or you may learn something new.

    In my narration, firepegs don’t die. Instead, they wake up (fire up), show their colors and fall asleep. You can change their colors, but the truly challenging part is changing the numbers on the links. Changing the numbers, you build a ‘social’ network. When the network is ready, you fire up a firepeg or two. They make their status updates available to their neighbors, the neighbors fire up in turn, and the network may begin oscillate in a way you wanted. Or not.

    Thank you for reading and please excuse my English (if any).

Leave a comment