@B55B55,
B55B55 wrote:I drew mine out on graph paper and also got a diamond.
I found that the first step had 4 passageways, (obviously) but then the second step had 12 new passageways as 4 of it's potential passageways were the original. I ended up with sixty something total passageways.
I think the tricky part is the existence of two passageway intersections.
When 4 passageways intersect you have to remove the area of 1 intersection. (If two passageways connect in a straight line, the intersection makes that equal to two passageways. Having another set on top means a loss of the size of one intersection). I ended up with 20 something of those.
However when two passageways intersect at a right angle they either don't lose any space at all, or they lose 1/4 of an intersection. (as they have 1/4 overlap and 1/4 of the space is not tunneled out)
My assumption is that the intersection of any two paths is squared out the way that it would be. That would mean that a two passageway intersection can be ignored. (I found there to be 12 of these though)
This looks like what I've drawn out. I get 25 4-way intersections, 12 2-way intersections, and 4 dead-ends/cul-de-sacs, with 64 passageway sections.
As B55B55 said, the questions come out at the 2-way intersections, and I would also say, at the dead ends. Both the 2-way intersections and the dead-ends come at the last step, where the LC says "with passages going 25 metres in each direction." Then it says, "each intersection is a 3-metre by 3-metre square." So the question is whether the 2-way intersections are intersections for purposes of the second quote, or whether the passages just go the 25 metres and leave the 1/4 intersection closed off. Looking at "Assume that 25 metres is the exact distance between the centres of each intersection," I would also wonder if the dead-ends hollow out the other halves of the terminal intersections, or whether they stop exactly at the 25 metre point.
If I hollow out both the 2-way and the dead-ends, I get 1***9. If I hollow out only the 2-ways, I get 1***5 and if I don't hollow out anything, I get 1***4.