This is the set of formulas for the Score of the game.
Reactions[]
Simple Reaction[]
The calculation for the score is given by 1.5 times the value of the atoms being combined plus 1. The result is rounded down to an integer.
score = floor(1.5 * (Z + 1))
Chain Reaction[]
To extend this to deeper reactions, we need to know that the value of reactions after the initial reaction is affected by a multiplier, which increases as the reaction goes deeper. The multiplier for a reaction is defined as,
M = 1 + 0.5 * r
where r is the rth reaction made. In this case, r = 2 represents the second reaction.
Two variables can be derived from this,
Sr = floor(M * (Z + 1)) B = 2 * M * (Zo - Z + 1)
where
- M is the multiplier,
- Z is the value of the middle atom,
- Zo ("Z outer") is the value of the outer atoms
The score is defined as
score = Sr if Zo < Z
Sr + B if Zo >= Z
The first score, in which the value of the outer atoms is less than the value of the center atom represents a normal reaction. The second, on the other hand, represents a +2 reaction, explaining the need for more points.
Example[]
Reaction forming an Oxygen (O, 8) atom and 81 points.
Imagine the circle starts off like this.
He, H, He, Li, H, H, Li, He, H, He
The reaction itself is displayed on the right, in which a Plus Atom is placed in between the two Hydrogen H(1) atoms to start a chain reaction.
We first combine the two Hydrogen H(1) reactions in a simple reaction, forming a Helium He(2) atom and 3 points.
S1 = 1.5 * (1 + 1) = 3
Two Lithium Li(3) atoms then fuse with the newly formed Helium He(2) atom for the second reaction.
- Z = 2
- Zo = 3
- r = 2
M = 1 + 0.5 * 2 = 2 Sr = 2 * (2 + 1) = 6
Since Zo >= Z, this is a +2 reaction, and
B = 2 * 2 * (3 - 2 + 1) = 8 score = 6 + 8 = 14
The score is now 17, and a Boron B(5) atom is formed.
Two Helium He(2) atoms fuse with the Boron B(5) atom for the third reaction.
- Z = 5
- Zo = 2
- r = 3
M = 1 + 0.5 * 3 = 2.5 Sr = 2.5 * (5 + 1) = 15
Since Zo < Z, this is a normal reaction, and
score = 15
The score is now 32, and a Carbon C(6) atom is formed.
Two Hydrogen H(1) atoms fuse with the Carbon C(6) atom for the fourth reaction.
- Z = 6
- Zo = 1
- r = 4
M = 1 + 0.5 * 4 = 3 Sr = 3 * (6 + 1) = 21
Since Zo < Z, this is a normal reaction, and
score = 21
The score is now 53, and a Nitrogen N(7) atom is formed.
Two Helium He(2) atoms fuse with the Nitrogen N(7) atom for the fifth and final reaction.
- Z = 7
- Zo = 2
- r = 5
M = 1 + 0.5 * 5 = 3.5 Sr = 3.5 * (7 + 1) = 28
Since Zo < Z, this is a normal reaction, and
score = 28
The reaction has created an Oxygen O(8) atom and formed a total of 81 points.
Others[]
- When a Black Plus is used, a simple reaction is performed on one of the atoms.
- At the end of the game, the values of all 19 atoms are added to the score.