Interstates in the grid

[Alps]

As best I can tell, this is a list of every Interstate number that is always in the grid (including suffixed routes) - meaning there is no lower-numbered route to the north/east and no higher-numbered route to the south/west as measured in direct E-W or N-S lines:
2, 4, 8, 10, 12, 14, 16, 22, 30, 72, 76, 78, 80, 88
5, 17, 19, 25, 27, 29, 39, 57, 79, 97

[Brandon]

Also, I-86 (W), and for now, until it is complete, I-86 (E), which would also include I-84 (E) until that time as well.  Should I-11 ever be extended to Phoenix, I-17 will fall off that list.  I-57 will fall off the list when the Arkansas section is designated and connected to the rest of it.

[Beltway]

How about I-66?

[Brandon]

How about I-66?

Same with I-68.

[sparker]

Also, I-86 (W), and for now, until it is complete, I-86 (E), which would also include I-84 (E) until that time as well.  Should I-11 ever be extended to Phoenix, I-17 will fall off that list.  I-57 will fall off the list when the Arkansas section is designated and connected to the rest of it.

If I-11 follows its presently likely path (Hassayampa corridor) down to I-10, I-17's presence on the list isn't in jeopardy.  Only if I-11 continues SE to the Casa Grande area (or, unfortunately, farther!) would that situation exist.  At present, nothing is written in stone regarding I-11's southern reaches.

[CNGL-Leudimin]

76 and 88 stand true for both iterations of each one. Also the Southern 87 for the time being.

Once 15 is extended all the way down to Naval Base San Diego, 5 will fall off the list.

[froggie]

How about I-66?

Same with I-68.

Using the OP's definition ("as measured in direct E-W or N-S lines"), there are segments of I-70 that are south of I-68...including the entire leg east of the 68/70 junction.  70 also dips south of 66's latitude in the St. Louis area, central Kansas, and Utah.

[GaryV]

How about I-66?

Same with I-68.

Using the OP's definition ("as measured in direct E-W or N-S lines"), there are segments of I-70 that are south of I-68...including the entire leg east of the 68/70 junction.  70 also dips south of 66's latitude in the St. Louis area, central Kansas, and Utah.

I took the definition to mean that, for example, from any point on I-70, a line drawn directly north would not intersect with any part of I-68.  If the line did intersect, the hypothesis fails. I think I-68 should be on the list.  I-66 as well.

If that's not the case, then there are other routes on the OP's list that fail.  For example, some portions of I-10 are at a latitude further north than the northernmost latitude of I-12.  And some portions of I-10 are at a latitude further south than the southernmost latitude of I-8.

[odditude]

additionally, under that definition, I-97 would fail as the entirety is east of I-99.

[sprjus4]

additionally, under that definition, I-97 would fail as the entirety is east of I-99.

I-99 is out of grid, I-97 is within the grid. I-99 fails, not I-97.

[sparker]

76 and 88 stand true for both iterations of each one. Also the Southern 87 for the time being.

Once 15 is extended all the way down to Naval Base San Diego, 5 will fall off the list.

Not necessarily; Caltrans generally specifies the endpoints of highways at the centerpoint of the interchange; the remainder are considered ramps only.  In this case, the southernmost 1/3 mile on a surface road is and has been locally maintained since the I-5/CA 15 (nee 103) interchange was built in the 60's. 

[Eth]

How about I-66?

Same with I-68.

Using the OP's definition ("as measured in direct E-W or N-S lines"), there are segments of I-70 that are south of I-68...including the entire leg east of the 68/70 junction.  70 also dips south of 66's latitude in the St. Louis area, central Kansas, and Utah.

I took the definition to mean that, for example, from any point on I-70, a line drawn directly north would not intersect with any part of I-68.  If the line did intersect, the hypothesis fails. I think I-68 should be on the list.  I-66 as well.

With that definition (which is also how I read it), I-68 still fails because of the presence of I-74, which is quite a long way to its south. I-66 should still be fine, though, since its west end is farther east than I-74's current east end.

[GaryV]

additionally, under that definition, I-97 would fail as the entirety is east of I-99.

I-99 is out of grid, I-97 is within the grid. I-99 fails, not I-97.

We only know that because I-99 was a latecomer with a mandated number outside the grid. 

But what about "original" routes?  Which is "out of grid":  I-71 or I-75?  By my "draw a straight line" interpretation of the rules, both fail because they cross.

With the "draw a straight line" interpretation, for any pair of routes that fail, both count as failing.

[Konza]

So I'm thinking that the "grid" is defined by east-west routes ending in zero and north-south routes ending in 5.  The only one of these routes that breaks this grid is I-85 west of its junction with I-75 in Atlanta.  By definition, except for I-85, these routes are compliant with the "grid".

An even numbered route defies the grid if it crosses one of the routes that end in zero or if you can easily travel north to cross a lowered number route or south to cross a higher numbered route.

The following additional east-west routes are compliant with the grid:
2
4
8
12
14
16
22
64
66
68
72
76 (both)
78
84 (east)
86 (both)
88 (both)
96

The following are not:
24 (north of I-40 west of Nashville)
26 (north of I-40 north of Asheville)
44 (original route OK, now crosses and goes south of I-40 in OKC)
74 (south of I-70 east of Indianapolis; if it ended there, there are worse things)
82 (north of 84)
84 (west) (south of 82; could be resolved by switching their route numbers west of their junction)
94 (drops south of I-90 in Chicago and Northwest Indiana)

An odd numbered route defies the grid if it crosses one of the routes that end in five or if you can easily travel east to cross a lowered number route or west to cross a higher numbered route.

The following additional north-south routes are compliant with the grid:
17
19
27
29
37
41
43
49
57
79
83
87
91
93
97

The following are not:
11 (totally east of I-15)
59 (east of I-65 north of Birmingham)
69 (a disaster south of Indianapolis; I'd suck it up as far south as Memphis)
71 (east of I-75 north of Cincinnati)
73 (is only compliant in Michigan, where it will probably never be signed)
77 (crosses I-81 and I-85, but the other routes are probably the problem here as I-77 pretty much goes north-south)
81 (see I-77; stays remarkably in grid other than it crosses I-77; I can live with this)
85 (from Atlanta to Montgomery is west of I-75)
89 (east of I-91 from I-91 to I-93)
99 (this is why politicians shouldn't do this...)

Different opinions welcomed...

[TheHighwayMan3561]

What about something like I-35, which doesn't actively cross any other x5s but has half the route west of I-29 and half the route east of I-37, I-45, and I-49?

[Brandon]

What about something like I-35, which doesn't actively cross any other x5s but has half the route west of I-29 and half the route east of I-37, I-45, and I-49?

As those do not cross I-35, I-35 is fine.