On a chess board, we place a pawn in its usual starting position, in the second row. We want to crown the pawn by taking it to the last row following the following rules:
- The pawn will advance as many squares as faces we get from the launch of a certain number of coins, which we assume balanced.
- We can use as many coins as we want, but once we choose the number of coins to be thrown we cannot change it throughout the game.
- We must reach the eighth row with the exact number of faces we need to crown.
- If we only get crosses or if we get more faces than we need to crown, the pawn will not move and we will launch again.
How many coins would you choose to try to crown in the least possible number of throws?
Extracted from the elmaquinadeturing page
the optimal number of coins to use is 4. If we choose less than 4 coins we throw so few that it will take us a long time to crown, but if we throw more than 4 the rule of "Crown with the exact number of faces" It can cause us to lose a good number of turns if we fall in a row close to 8.
The demonstration is extensive and is included in this document written by Javi Oribe.