Big Walk number puzzle: A few small hints and the full solution

Early on in Big Walk, as you and your pals are scurrying around the world solving puzzles, you might come across a curious sight: a structure near the beach with an oblong prize (here at PC Gamer we call it a nubbin) inside a frosted glass container. Hanging on a hook above it: a sign with some numbers on it. Curious!
You’ve probably already seen a nubbin in a similar container, which could only be accessed when one of your companions held down a button in a nearby location. But what do these two four-digit numbers mean? And where’s the button?

If you’re stumped with this numbers puzzle, as we were for a while, we’re happy to help.
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Since Big Walk is best when you figure puzzles with your friends instead of by reading guides, I’ll ease you into the solution to this number puzzle by giving you progressively more explicit hints below. This way you can get some help without completely spoiling the solution, if you like.
Hints
Hint 1:
When you first find this number puzzle, most likely just after you’ve completed the tutorial puzzles, you won’t be able to solve it. It’s just that simple. The best advice is to leave it for now and come back to it later, after you’ve solved five other puzzles and completed the red tower.
Hint 2:
When you’re looking around the rest of the world, keep those numbers in mind. Specifically, the format: two four-digit numbers. Maybe you’ll see something elsewhere that looks like it’s related.
Hint 3:
You’ll need a specific item to make sense of those numbers. There are actually two different items that can be individually used to help you with the number puzzle.
Hint 4:
The numbers 4166 and 1899 are coordinates, latitude and longitude, and they point to the button’s location on the island.
Hint 5:
There’s a map that can be used to find the coordinates, and there’s a device that displays its current coordinates on a screen, like a GPS. Either of those can be used to solve the number puzzle.
OK, that’s enough hints. Here’s the solution:
Solution
First, you can find the map, which requires placing five nubbins on the red tower’s roof. The map room will then open up right next to the starting hub, which features a large map on the floor, and a portable, foldable map and compass.
With the map opened in your hands, you can follow the longitude (the numbered lines on the sides) of 41 and the latitude (the numbered lines on the top and bottom) of 18. Where they meet on the map is the grid square to search for the button, which is east and south of the starter hub. The “66” in 4166 refers to a more exact measurement than the map shows, meaning it’s about two-thirds of the way south from the top of the grid, and 99 means it’s about as far east as you can be in the grid, right along the gridline.
Enlarge the image below by clicking on the arrows on the lower-left corner, if it helps.

That’s where to look! You’ll find a small button carefully camouflaged behind a rock. Someone will have to hold down the button while another player grabs the nubbin at that puzzle building when the glass container opens, so make sure you’ve got walkie-talkies with you.
The other way to find the button (and the more fun way, in my opinion) is by using the GPS device. This item will take longer to find than the map: you’ll need to visit the green tower, which is in the same area you’ll eventually find the button, and just outside it you’ll see a red frame holding the GPS (and another sign with more numbers on it).

You can hold the GPS up to friends to show current coordinates, or stick it on someone’s backpack.
With one player wearing the GPS on their back, another player can direct them which way to go. Just keep your eyes on the numbers: as you move across the island, the GPS readout will tell you if you’re getting closer or further from the location of the button. Happy walking!



