Philosophical Riddles for Chess Players

by Arne Kaehler
5/26/2020 – The logic riddles series has a new companion with the philosophical section. The riddles are all solvable but also debatable and paradox. One solution is not necessarily the only one and various ways to solve a puzzle can be found. The first riddle in this new series concentrates on a solution, which might be clear for some people, but wouldn't make any sense for others. Give it a try, think about the options to solve the riddle and you are more than welcome to post your solution in the comment section.


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White always wins

The two chess grandmasters, Fritz Seventeen and Houdini Komodo, were playing against each other for many years to find out who was the best chess player in the world. But their score was absolutely equal, because the player with the white pieces always won. In order to settle the question of who the best player was once and for all, a tournament was organized with the first prize being millions of dollars, and the second place winning nothing.

The tournament rules were very simple. If a player won two games in a row he won the tournament. After each game, the colour of the pieces changed. Unfortunately, the competition took the expected outcome.

After 100 games both players had won 50 of their games with the white pieces. Not only did they win with ease, the player with the black pieces was basically without a chance every time. In order to finally end the tournament, the managers of the competition made a decision.

One last decisive game will be played tomorrow. Fritz, the player who started the tournament with the white pieces, will choose one of two small paper rolls. On one paper roll the word "black" is written, on the other one the word "white". Whatever paper roll he takes, he will receive the colour written on the roll to play the game.

Both players protested that the outcome would be pure luck now. Whoever gets the white pieces will win. But the tournament managers stood by their decision.

Little did Fritz know that Houdini and the tournament managers were working together, trying to manipulate the outcome of the tournament. Houdini was happy to give the prize money to the managers if he would succeed. He didn't care about the money, he only wanted to win. It was Houdini's idea to end the tournament with one last game.

That evening, before the last game started, Fritz went to the hotel bar. All of a sudden the second of Fritz ran into the hotel bar and sat right next to him to tell him something important: "Fritz, I remained in the tournament hall because the managers asked me to help them set up the chairs for the audience, and while I was doing this I heard some voices coming from the managers' room. I went over and could peek inside the half-open door. To my big surprise I could see the tournament managers writing the colours on the small paper rolls. Can you believe it? They wrote BLACK on both rolls! They want you to lose Fritz!"

Fritz thought for a short moment and said to his second:"Thank you for telling me. Have no fear, all will be fine. I know what to do!"

At that time Houdini went to the tournament hall to see the managers. He asked them:"Did you write black on both paper rolls as I told you?" The managers answered:"Yes, we did, Houdini". Houdini continued: "And did Fritz's second see that you were writing the words down on the paper rolls?" "Yes, Houdini, and one of us followed him and confirmed that he told it to Fritz, just as you predicted it to happen." 

Houdini sat down with a smile."Wonderful. Fritz is a very smart fellow. Now proceed with the last step, so I can win the game tomorrow." The managers nodded and took the necessary step.

The next day, to Houdini's and the managers big surprise, Fritz Seventeen could win the tournament with the white pieces.

What did he do?

Keep in mind, one last necessary step was taken by the managers and Houdini to guarantee his success, which backfired heavily. Logic doesn't help here, but it should be used in a good dose. Many solutions are possible, but one in particular is used for the outcome.

The unrealistic fact, that the players always win with the white pieces, carries the puzzle forward and shouldn't be taken too seriously. In the end, Fritz wins with the white pieces anyway.

I used the names Fritz, Houdini and Komodo for no other reason than to promote them here! After all, on May 27 we have our big discount day!

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The dumb pawn solution

I believe everybody who shared their ideas wrote in the comment section found the correct solution but there were plenty of different formulas to arrive at the solution.

The riddle ends with the dumb pawn having exactly zero ducats left. Well, let us wrap it up from this number, because it leads to the overall result.

If the pawn had exactly nothing left, he was paying the ♞ 24 ducats. This means, he doubled this amount earlier, so he had twelve ducats. Now we better understand, why he is a bit of a simpleton. After running up and down the board and having less money than he had at the beginning he should have understood that this deal might not end well for him.

He gave 24 ducats to the ♞ before that, which makes 36 ducats (12+24). That was doubled, so he had 18 ducats (36 divided by 2). The last and final step is to give another 24 ducats to the ♞ which is exactly 42 ducats and half of 42 is 21. In the very beginning, the dumb pawn had 21 ducats.




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