Cogs Toontown Rerwritten

Cogs are the main antagonists of Toontown Rewritten. They are corporate robots with the objective to convert Toontown into a corporate dystopia. Their corporate ladders comprise of fourteen Cogs each that normally vary from level 1 to level 21 as well as a boss Cog. Cogs use a set of attacks to drain Toons' slaff and sadden them; stronger Cogs tend to have higher health and stronger attacks. However, Cogs cannot take a joke, and therefore they explode when they laugh upon being affected by Toons' arsenal of gags.

History

On April 19, 2014, the Cogs invaded Toontown for the first time when they made an unexpected interruption during the Toon Council Presidential Elections by unleashing an invasion known as Doomsday to exercise ambush marketing. Sometime after Doomsday, the Cogs now roam the streets of Toontown to take over Toon Buildings by dropping Cog Buildings onto them, and have established their own Cog headquarters that are connected to some streets.

They are the lowest tier Cogs on the corporate ladder.

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Cogs list size

Level 1 Cogs are tier 1 Cogs with a total health of 6.
Level 2 Cogs are tier 1-2 Cogs with a total health of 12.
Level 3 Cogs are tier 1-3 Cogs with a total health of 20.
Level 4 Cogs are tier 1-4 Cogs with a total health of 30.
Level 5 Cogs are tier 1-5 Cogs with a total health of 42.
Level 6 Cogs are tier 2-6 Cogs with a total health of 56.
Level 7 Cogs are tier 3-7 Cogs with a total health of 72.
Level 8 Cogs are tier 4-8 Cogs with a total health of 90.
Level 9 Cogs are tier 4-9 Cogs with a total health of 110.
Level 10 Cogs are tier 4-10 Cogs with a total health of 132.
Level 11 Cogs are tier 4-11 Cogs with a total health of 156.
Level 12 Cogs are tier 5-12 Cogs with a total health of 196.
Level 13 Cogs are tier 6-13 Cogs with a total health of 224.
Level 14 Cogs are tier 7-14 Cogs with a total health of 254.
Level 15 Cogs are tier 8-14 Cogs with a total health of 286.
Level 16 Cogs are tier 9-14 Cogs with a total health of 320.
Level 17 Cogs are tier 10-14 Cogs with a total health of 356.
Level 18 Cogs are tier 11-14 Cogs with a total health of 394.
Level 19 Cogs are tier 12-14 Cogs with a total health of 434.
Level 20 Cogs are tier 13-14 Cogs with a total health of 476.
Level 21 Cogs are tier 14 Cogs with a total health of 506.

Cogs have certain amount of health that depend on their level and are determined by certain mathematic formulas. The table below shows the health of every existing Cog level.

Level	Health
Level 1	6
Level 2	12
Level 3	20
Level 4	30
Level 5	42
Level 6	56
Level 7	72
Level 8	90
Level 9	110
Level 10	132
Level 11	156
Level 12	196
Level 13	224
Level 14	254
Level 15	286
Level 16	320
Level 17	356
Level 18	394
Level 19	434
Level 20	476
Level 21	506

Formulas

Level 1-11 Cogs

The formula for health of Cogs from levels 1 to 11 can be:

f(x) = x² + 3x + 2

or in a simplified way:

f(x) = (x + 1) * (x + 2)

where x is the Cog's level and f(x) is a function that returns the Cog's health value.

For example, the formula works in the following method to determine the health of level 4 Cogs.

f(4) = (4 + 1) * (4 + 2)

f(4) = (5) * (6)

f(4) = 30

Level 12+ Cogs

Level 12 Cogs previously had a 10% boost in health, putting them at 200. As of the 3.0.0 update that was released on December 3, 2021, which introduced balancing changes, level 12+ Cogs now have a unique formula to determine their health.

The formula for health of level 12+ Cogs can be:

f(x) = x² + 3x + 16

which is the same as the formula for levels 1 through 11, but has an increase of 14 units in Y value for every unit of X. Unlike the former formula, it has no roots.

The simplified formula can also be represented as:

f(x) = (x + 1) * (x + 2) + 14

For example, the formula works in the following method to determine the health of level 16 Cogs.

f(16) = (16 + 1) * (16 + 2) + 14

f(16) = 17 * 18 + 14

f(16) = 306 + 14

f(16) = 320