Forum:Pop the balloons ( googology challenge )

Capital letters are balloons, except for P which is a pin, and S is the score, it begins at 0

At each step, gently push the balloons to the left, so whichever balloon is in contact with the pin "pops" or disappears, what happens next depends on the color of the balloon

Red ballons R = Increase S by 1 Blue balloons B = Spawns S Red Balloons where they pop Green balloons G = Spawns S Blue Balloons where they pop Yellow balloons Y = Spawns S Green Balloons where they pop

Note: Spawning ballons will push existing balloons to the right, if there are any, to make enough room for themselves The challenge is this: how much score would you gain from clearing the following wave of ballons?

PRBGY

If you give up scroll down for the answer

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Its, in fgh:

$$f_3(8)$$

Or, bound using tetration

$$^92 < \ S < \ ^{10}2$$