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for a personal usage:
The Big Game in the Casino of Many Squares.pdf
The declaration to the Big Game.pdf
If you think that it is not possible for anyone to successfully finish the Big Game you can look at two examples of the successfully finished the Big Game attached below!
Two Examples of the Big Game.xlsx
A casino called the Casino of Many Squares has a playing hall with 64 gaming tables. This playing hall was built for the Big Game that consists of 4096 (4096 = 64 x 64) individual bets and is always played by a group of 64 players. There are four basic rules of the Big Game that must be complied with.
- Each of 64 players must bet exactly once at each of the 64 gaming tables.
- All tokens have the same value. Any bet ends up winning (paid bets) or losing (loosing bets). Zero bets are not allowed. The pay-out ratio for all bets is 1:1.
- The sum of squares of all 64 bets at each of 64 gaming tables must be equal to 67600.
- A difference between all paid bets and all losing bets at each of gaming tables must be equal to 900.
In case, any of these rules are not followed all players lose their tokens and the game ends. However, if all players achieve exactly the same profit in the end of a game (paid bets minus losing bets) each of them will get a bonus 900 x 64 tokens.
(See The Bonus Game in Two Examples of the Big Game.xlsx)
There is a plaque in a foyer of the Casino of Many Squares. It tells the Legend about the Big Game. Nobody knows if it is true but some players believe it is a clue for success in the game that might bring a lot of fame.
(To see the plaque - download the file - The Big Game in the Casino of Many Squares.pdf)
To support spreading the Legend about the Big Game the Casino of Many Squares announced a special bonus called The Prize for the Symmetry in the Big Game
It represents the bonus 1,000,000 tokens per player!
It means the total bonus sum is 64,000,000 tokens!
(See the Prize for the Symmetry in Two Examples of the Big Game.xlsx)
The price will be awarded to each of 64 players of any groups which will fulfil 3 conditions:
- The group of 64 players finished the Big Game.
- The group can be divided in such two subgroups of 32 players that there is no difference between total results of players of both subgroups. It means they are symmetrical.
- The sum of squares of won tokens of the individual players plus the sum of the squares of lost tokens of the individual players in the subgroup is equal to 64,000,000.
It is said that the number 64,000,000 is a clue
The number 64 allegedly expresses the square of the number of losers in this game (total 8 players) and 6 zeroes symbolize that only 6 out of 64 players end this game with zero (in each of both 2 subgroups 3 players).