The Collatz Conjecture is a famous problem in mathematics.
The conjecture states that starting from any number n, repeatedly calling ƒ(n) (using the result as the next value of n)
will always reach 1.
ƒ(n) = {
n/2
(3n+ 1)/2
, if n is even
, if n is odd
For example, Starting with n = 5 yields the sequence, ƒ(5) = 8, ƒ(8) = 4, ƒ(4) = 2, ƒ(2) = 1.
(Note that this is the 'shortcut' version of the Collatz function.)
To start checking numbers, add clocks to the grid by left clicking any cell and choosing a type.
Whenever a clock completes a cycle, it will perform an action based on its type and its upgrades.
After buying a clock, click it to open its upgrade menu. Hover over an upgrade to see its description.
Right click a clock to pause/unpause or scrap it (for half the amount spent on upgrades).
Drag a clock to move it to a different cell.
When a Producer cycles, if n is not 1, it updates the value of n to ƒ(n) and adds $1 to your money.
When a Verifier cycles, if n is 1, it updates n to Checking+1.
Get Checking as high as possible. This represents a lower bound for a counterexample to the Collatz Conjecture.
Get Checking to increase as fast as possible by optimizing the placement of your clocks and how you spend your money.
Achievements: coming soon™
Hover over buttons / upgrades to see their descriptions.
Options and progress will be saved automatically.
When the game is in the background, the clocks will appear paused but the game will still progress:
Every 10 seconds, 10 seconds gets simulated, and any remaining time is simulated when the game is brought back into focus.