Final Fantasy X-2/Sphere Break

Sphere Break is a minigame within the role-playing game Final Fantasy X-2. A bit like Sudoku, the game has a numerical grid that has to be dealt with using a set of rules. The mechanics of the minigame are purely mathematical, relying on sums and multiplications; the aim is to create the most multiples of a "core number" by combining numbers of the 16 coins on the board.

Coins
Coins are numbered from 1 to 9 and possess several different attributes that can help you in the Final Fantasy X-2 or in the Sphere Break Minigame itself (Free magic Item, Free potions, Echo, + coins, quota multipliers, …)

Core Break
A Core Break happens when the player selects coins that added to each other form a sum that is a multiple of the number rolled by the Core Sphere. The player with the coins has to obtain a Core Break in a set limit of time or he loses the game. A core break ends a turn in the game.

Center Coins / Entry Coins
The player playing against the dealer (owner of the core sphere) selects 4 coins to bet. They will be his entry coins and will be placed in the center. During the game, every time the dealer rolls a number on the core sphere, his opponent has to pick at least one entry coin to start his turn.

Border Coins
At each turn, a number of coins between 0 to 12 coins surrounds the center coins and the core sphere. The player uses them to make a Core break. At each turn, any coin not used in a core break is increased in value by one. If it had a value of 9 before, it is removed from play as they cannot be a value of ten. Coins used in a core break are also removed. Empty spaces are filled (or not) randomly, with a new coin valued from 1 to 9.

Game mechanics

 * 1) Like a dice, the dealer makes his Core Sphere produce a number from 1 to 9 for a set number of turns, i.e. 20 turns
 * 2) For each turn, the player has to use at least one of his center coins which on the tournament of Final Fantasy X-2 are preset 1,2,3 and 5 with multiplier Echo
 * 3) Each turn has a set time limit from (60 seconds, 30 seconds..) and the player has to produce a multiple of the Core Sphere within it. If he fails he loses the game and also loses the center coins he bet
 * 4) Each game has a "Quota", i.e. a set number of coins that needs to be used in the games set umber of turns. If all turns are used and the player did not complete his quota he loses the game and also loses the center coins he bet
 * By using the multipliers and other coin attributes players can beat dealers with very difficult Core Spheres. The current champion Shinra has a quota of 100 coins that has to be obtained in just 15 turns with a time limit per turn of 45 seconds.

A sample game

 * Quota: 30 coins, Turns: 20 turns, Time limit per turn: 60 seconds (a very easy game with low quota, lots of turns and large time limit per turn)
 * 1 - For the first turn, the dealer rolls out a number from 1-9, i.e. 7
 * In his first turn the player needs to find a multiple of 7 by adding the center coins (1,2,3, and 5 with multiplier echo) and the 0-12 border coins (randomly set).
 * Here the player could just use center coins (2+5) but this is not to the player's advantage because center coins do not add any coins to the quota of 30 coins he has to use before his 20 turns are complete. The player has to pick one center coin, so let's pick 2 (Sum=2)
 * Now the player looks at the border coins and tries to get as many border coins he can to make a multiple of the core sphere's 7. Since he already picked a 2 the maximum sum of the border coins he can pick has to be either 5 or 12 or 19 etc... to yield a multiple of 7 such as 7 or 14 or 21 etc...
 * The player picks 3 border coins: 8, 8 and 3 making his total Sum = 2 + 8 + 8 + 3 = 21 and obtains a successful turn, i.e., a sphere break
 * His quota is now equal to 3 coins and his multiplier was 3 because he closed the turn with 21 which is 3 * 7 . The multiplier is important because one of his center coins has the multiplier echo attribute and will help augment the player's quota in his next turn
 * 2 - On the second turn the Core Sphere rolls a 1 which is good for the dealer and bad for the player
 * Faced with a 1 from the core sphere the player is forced to pick only center coins, as any number he picks will be a multiple of 1 and he has to start by picking a center coin. This means he will not get any extra coins to add to his quota this turn.
 * As noted above, any center coin (1,2,3 and 5) will end the turn. A clever player would use the multiplier echo to his advantage here and pick the 3 center coin. This will make his multiplier for his second turn to be equal 3 which is what 3 * 1 amounts to.
 * Note that the turn ends with the same multiplier as the last turn: 3. This means the player has a multiplier echo
 * The turn ends with a quota of 3 (no border coins were added) and a multiplier echo of 1
 * 3 - For the 3rd turn the Core sphere rolls a 2
 * A clever player would pick his mandatory center coin to be odd because any coin that is even will end his turn. Our player picks 1
 * For the border coins, our player can now keep on picking odd coins but to take advantage of the multiplier echo he needs to stop when his sum totals 6 which is 3 * 2 and gives him another multiplier echo.
 * Our player picks a 5 border coin making his sum equal 1+5 = 6 and making another multiplier echo
 * The turn ends with a quota of 4 plus the echo bonus of 2 * his quota on this turn which is 2*1, giving him a total quota of 6 and a new multiplier echo of 2
 * 4-20 - The game proceeds until either all 20 turns are completed or the quota of 30 coins is fulfilled. If the player fulfills his quota before the end of 20 turns he wins the game and all the prizes yielded by the border coin attributes.