Give each state an Interstate that well represents the state.

[thspfc]

Simple: Assign all 50 states a 2di Interstate, without using the same number twice. I'll start:

AL: I-65
AK: I-A4
AZ: I-17
AR: I-49
CA: I-5
CO: I-76 (W) (would be I-70, however then Kansas would get I-35, and in turn Iowa gets I-80, leaving Nebraska with a tiny sliver of I-76)
CT: I-84 (E)
DE: I-95* (only one)
FL: I-4
GA: I-75
HI: H-1
ID: I-86 (W) (I-84 sacrificed in favor of OR)
IL: I-57
IN: I-69 
IA: I-35
KS: I-70
KY: I-64
LA: I-12
ME: I-95*
MD: I-97 
MA: I-91
MI: I-96
MN: I-94
MS: I-55
MO: I-44
MT: I-90
NE: I-80
NV: I-15
NH: I-93
NJ: I-78
NM: I-10 (it should be 40 so that TX gets 10, but that would cause problems for Oklahoma)
NY: I-87 (N)
NC: I-85
ND and SD: I-29 (I don't believe it can be done if these states are separate, so I'm lumping them together since they have basically the same name)
OH: I-71
OK: I-40
OR: I-84 (W)
PA: I-76 (E)
RI: I-95*
SC: I-26
TN: I-24
TX: I-20, though 10 is more fitting
UT: All things considered, is not possible without sacrificing another state. Otherwise it would be I-15.
VT: I-89
VA: I-81
WA: I-82 (should be 90, but Montana would then screw everything up)
WV: I-77
WI: I-41
WY: I-25

So all in all, it can be done at the expense of four states: UT (in my example, but that could be a host of others such as CO, NE, KS, IA), ND or SD (I-29 can be assigned to one of the two), and two the three one-2di states (ME, RI, DE on I-95). Try to do it better if you can.

[hotdogPi]

74 to IA, 35 to MN, 94 to ND

[thspfc]

74 to IA, 35 to MN, 94 to ND

Yeah, I totally missed that  I forgot that 74 entered Iowa.

[webny99]

If you want the route chosen to be representative of the state, you're going to end up with duplicates. If you don't want duplicates, you're going to end up with routes that don't really represent the state.

New York is one state that's easy; it's I-87 pretty much regardless.

[Beltway]

Simple: Assign all 50 states a 2di Interstate, without using the same number twice. I'll start:

VA: I-81

I-81 is all western and hilly to mountainous terrain.

I would use I-64 -- western mountains to the piedmont to the sea.  The state capital, the old state capital, the James River, Chesapeake Bay, the coastal and major port cities.

[jp the roadgeek]

Hey!!  You used I-84 and I-76 twice.  Yeah, they are all different routes, but it's the same number. To eliminate it, I'd use I-91 for CT and I-79 for PA.

[sprjus4]

Simple: Assign all 50 states a 2di Interstate, without using the same number twice. I'll start:

VA: I-81

I-81 is all western and hilly to mountainous terrain.

I would use I-64 -- western mountains to the piedmont to the sea.  The state capital, the old state capital, the James River, Chesapeake Bay, the coastal and major port cities.

Then what would Kentucky be?

I see it though. I'd similarly say for North Carolina, I-40 over I-85. I-40 traverses from the western mountains near Tennessee, through Asheville heading eastwards into the plains, thru the major Piedmont metro areas, Winston-Salem and Greensboro, then onto Durham and Raleigh (the state capital), and towards the Atlantic to Wilmington, the state's largest port facility (nowhere near as impressive as Hampton Roads though), and the largest (?) coastal city in NC.

I-85 just goes through the center of the state mainly, connecting Durham, Raleigh (via I-40), Greensboro, Winston-Salem (via I-285), and Charlotte, and a pass through route for long-distance traffic.

I-26 for South Carolina makes since - same thing - western mountains to coastal sea.

[hotdogPi]

8 to CA, 5 to OR, 84 (W) to UT

[NE2]

NJ: I-84

[Beltway]

Simple: Assign all 50 states a 2di Interstate, without using the same number twice. I'll start:
VA: I-81

I-81 is all western and hilly to mountainous terrain.
I would use I-64 -- western mountains to the piedmont to the sea.  The state capital, the old state capital, the James River, Chesapeake Bay, the coastal and major port cities.

Then what would Kentucky be

I was thinking that the "without using the same number twice" referred to any state, but now I see that apparently it applies to all.

So that would mean that only one state would be assigned I-64.

[J3ebrules]

I'm gonna argue that NJ deserves I-95, since it's pretty much the bulk of the New Jersey Turnpike - which pretty much defines our state. And predates the Interstates (so technically, I'm also arguing for I-95 on the "we had it first"  doctrine).

I78. What the hell are we going to do with I-78, go from Newark to the Poconos?? 

Rhode Island and Maine can be sacrificed, although I'm sorry to see them go because they are nice states. Delaware we can slay with impunity because DE1/US 13 should be upgraded to an Interstate anyway because traveling to the DE shore and Virginia Beach is physically painful.

[sprjus4]

traveling to the DE shore and Virginia Beach is physically painful.

It's a nice drive, but the painful part is seeing nothing higher than 55 mph for hundreds of miles. If the speed limit was 65 mph in the rural areas, it'd be perfect.

Numerous times I've been cruising along enjoying the drive, then look down at my speedometer and I'm going 70 mph. Kick it down to 55 mph, and it's a snooze fest. At least with a 65 mph speed limit, 70 mph would be very reasonable and acceptable, and many parts of the route could easily handle that.

Then there's roads like US-301 on Maryland's eastern shore where it's under-posted at 55 mph, and it's easy to hold 70 mph for the entire stretch with no issues, especially with the fact that it's extremely rare for someone to be going under 65 mph and easy to jump into a flow of 70 mph traffic.

[Scott5114]

NM: I-10 (it should be 40 so that TX gets 10, but that would cause problems for Oklahoma)

30 to AR, 49 to MO, 44 to OK, 40 to NM, 10 to TX.

44 works better for OK than 40 anyway since it hits three of the four largest cities in the state, as well as the western plains and Green Country. Though one could make an argument that 44 represents MO better than 49 does.

[J3ebrules]

traveling to the DE shore and Virginia Beach is physically painful.

It's a nice drive, but the painful part is seeing nothing higher than 55 mph for hundreds of miles. If the speed limit was 65 mph in the rural areas, it'd be perfect.

Numerous times I've been cruising along enjoying the drive, then look down at my speedometer and I'm going 70 mph. Kick it down to 55 mph, and it's a snooze fest. At least with a 65 mph speed limit, 70 mph would be very reasonable and acceptable, and many parts of the route could easily handle that.

Then there's roads like US-301 on Maryland's eastern shore where it's under-posted at 55 mph, and it's easy to hold 70 mph for the entire stretch with no issues, especially with the fact that it's extremely rare for someone to be going under 65 mph.

Yes... and I'm still salty as I pay off my $198 speeding ticket from that area...   

[NWI_Irish96]

The tasks of "well represents the state" and "can't use the same number twice" are conflicting.  I-69 is at best the 3rd or 4th best representation of Indiana. 

[Flint1979]

I-75 represents Michigan better than I-96 does regardless of I-96 traveling close to or through the largest city in the state, the state capital and the second largest city in the state. I-75 is by far the busiest interstate in Michigan and has the Mackinac Bridge along its route.

[GaryV]

Simple: Assign all 50 states a 2di Interstate, without using the same number twice.

The OP's directions are quite different than the thread title.

The title should have been, "Give each state an Interstate without duplicating numbers"

[Konza]

If the goal is to collect one sign from each state without duplicating, I'd offer:

AL:  59
AK:  choose one of the Alaska-only routes
AZ:  17
AR:  30
CA:  8
CO:  76
CT:  84
DE: (95) Only mainline Interstate in DE
FL:  4
GA:  16
HI:  Same as AK, but why not H-3 because it's gorgeous and I'm not using 3 elsewhere...
ID:  86
IL:  57
IN:  69
IA:  74
KS:  35
KY:  65
LA:  12
ME: (95) Only mainline Interstate in ME
MD:  68
MA:  93
MI:  96
MN:  90
MS:  22
MO:  49
MT:  15
NE:  80
NV:  11
NH:  89
NJ:  78
NM:  40
NY:  87
NC:  77
ND:  94
OH:  71
OK:  44
OR:  5
PA:  81
RI: (95) Only mainline Interstate in RI
SC:  26
SD:  29
TN:  24
TX:  27
UT:  70
VT:  91
VA:  64
WA:  82
WV:  79
WI:  43
WY:  25

0 and 5 routes that could be substituted here:  10, 20, 45, 55, 75, 85

[Life in Paradise]

I would also give Nevada I-11, but for Utah, put I-15 there.  Of course I-11 doesn't best represent Nevada (yet), but it isn't used anywhere else.