Alan Wake 2 car and bicycle wheel cult stash puzzle solution

For the Alan Wake 2 car and bike stash, you need to solve another number puzzle to reveal the stash's three-digit padlock code. You'll know roughly what to expect if you solved the previous battery amp puzzle in Alan Wake 2, though this cult stash tasks you with figuring out the code based on the number cars in a factory filled with 200 cars and bicycles and 754 wheels between them. Why the Cult of the Tree uses these algebra puzzles for their supply stashes remains a mystery, but I've run the numbers for this puzzle and have the answer to the Alan Wake 2 car and bike stash below.

Just like the Alan Wake 2 battery stash puzzle, figuring out the number of cars in this factory requires a bit of algebra. In short, if all 200 vehicles in the factory were cars, there would be 800 wheels. 800 – 754 = 46, which is the wheel difference created by some of the vehicles being bicycles and not cars. Divide 46 wheels by 2 to get 23 bicycles. Finally, 200 – 23 = 177, which is the number of cars. Here's the full proof of how I got the answer of 177:

1. The start of the puzzle explains that there are 200 vehicles in this factory, where vehicles refers to a mix of cars (c) and bicycles (b). Therefore, c + b = 200
2. Next, the question explains that each car has four wheels, each bike has two wheels, and there are 754 wheels in the factory. Therefore, 4c + 2b = 754
3. The question then asks how many cars there are, so using the above equations, we need to figure out the value of c. Start by rearranging the first equation then substitute it into the wheel equation to figure out the value of b:
   c + b = 200
   c = 200 - b
   
   4c + 2b = 754
   4(200-b) + 2b  = 754
   800 – 4b + 2b = 754
   800 – 2b = 754
   800 = 754 + 2b
   2b = 46
   b = 23
4. Substitute b into the original equation to get the answer: c = 200 – 23 = 177
5. Substitute it all into the wheel equation to check:
   4(177) + 2(23) = 708 + 46 = 754

Yes, I know it's a lot if you have zero maths ability but you'll have to complete al of these if you want to get the Alan Wake 2 Lighthouse Key which is the reward for opening all the stashes. 

There are loads of other collectibles to search for as well, such as Alan Wake 2 lunch boxes when you're playing as Saga, and Alan Wake 2 Words of Power for when you're Alan himself.

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