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One of the features of the Wall of Stone spell is to bridge a gap (emphasis added):

A nonmagical wall of solid stone springs into existence at a point you choose within range. The wall is 6 inches thick and is composed of ten 10-foot-by-10-foot panels. Each panel must be contiguous with at least one other panel. Alternatively, you can create 10-foot-by-20-foot panels that are only 3 inches thick.

[...]

The wall can have any shape you desire, though it can't occupy the same space as a creature or object. The wall doesn't need to be vertical or rest on any firm foundation. It must, however, merge with and be solidly supported by existing stone. Thus, you can use this spell to bridge a chasm or create a ramp.

If you create a span greater than 20 feet in length, you must halve the size of each panel to create supports. You can crudely shape the wall to create crenelations, battlements, and so on.

So, I want to bridge the longest possible gap using this spell. Obviously I will choose to use 10-foot-by-20-foot panels, connected lengthwise. However, I will need to "halve the size of each panel to create supports". So, do I end up with 10-foot-by-10-foot panels (for a total reach of 100 feet), or 5-foot-by-20-foot panels (for a narrower bridge reaching 200 feet)? Or something else? What is the longest gap I can bridge with these panels?

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The rules don't say -- ask your DM.

Either of the answers you proposed:

do I end up with 10-foot-by-10-foot panels (for a total reach of 100 feet), or 5-foot-by-20-foot panels (for a narrower bridge reaching 200 feet)

seems reasonable to me. But it's up to the DM to interpret the rules when they're ambiguous, and we can't tell you how your DM should rule.

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