Logic Riddles for Chess Players (6)

by Arne Kaehler
7/27/2020 – The main theme for this logic riddle is the world of Combinatorics. Although it requires some calculations, it is a lot of fun to try to correctly compare probabilities. Of course, we also have the solution for Logic Riddle #5 available!

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The fair fair?


Once a year, a big chess fair takes place on the chessboard, organized by the black king. It consists of some fun rides, a great variety of food stands (mostly fried liver for some reason) and the highlight: four games of chance! If you are older than 18 years, you can join the games and try your luck!

The name of the four games are:

  • The ten white pawns
  • Black or White
  • Numbers of fortune
  • The dice

The Ten White Pawns

There is one box, containing ten white pawns. Each pawn has a different number written underneath it. The numbers are 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Four random pawns are picked from the box to build a four-digit number.

You can bid one ducat to guess the correct number in the correct order. If you guess the number correctly, you will win 4000 ducats.

Black Or White

A spinning wheel which shows the colours black and white equally — a roulette wheel without the zero — has to be turned ten times. If you are able to get the white colour ten times in a row, you will receive 1000 ducats. One attempt costs 1 ducat.

Numbers Of Fortune

Here you can see four boxes, where each box holds ten white pawns with a different number from 0-9, just like in the game "The Ten White Pawns". Now one pawn is chosen from each of the four boxes. If a pawn has a number that had already been picked, it will be exchanged for a different pawn. This continues until four pawns are picked with four different numbers.

Whoever can guess the four numbers correctly, without needing to guess the particular order of the numbers, wins 500 ducats, by paying 2 ducats.

The Dice

Four dice are rolled (numbers 1-6) and if you can guess the correct numbers being rolled, without any particular order, you can win 500 ducats for an entry fee of five ducats.

Which of the games is by far the most profitable, comparing the entry fee and the amount you can win?

The games in table form:

Game Name Entry per game Winning
The Ten White Pawns 1 Ducat 4000 ducats
Black Or White 1 Ducat 1000 ducats
Numbers Of Fortune 2 Ducats 500 ducats
The Dice 5 Ducats 500 ducats

The riddles are pretty interesting to solve and require mathematics. I worked for an Online Casino for a couple of years, and all the games you could play online had a certain "RTP" percentage, which means “return to player”. 

If you do the math correctly, you can find out the RTP % of each game.

Solution to the last riddle: How many colours?

Thank you once again for your participation in the comment section! It shows that the logic riddle section is enjoyable.

Certainly you were all correct. The answer is simply “four colours”. How this might look like is shown in the picture below:


Arne Kaehler, a creative mind who is passionate about board games in general, was born in Hamburg and learned to play chess at a young age. By teaching chess to youth teams and creating chess-related videos on YouTube, Arne was able to expand this passion and has even created an online course for anyone who wants to learn how to play chess. Arne writes for the English and German news sites, but focuses mainly on content for the ChessBase media channels.


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