Okay this is messing with my head.

Arkansas borders 6 states and it's possible to travel south to enter all of them.

@drewphish

Now I want to know how universal this is. Wisconsin borders 4 states and it's possible to travel south to enter all 4. Illinois borders 5 states and only Wisconsin is inaccessible going south. But you can reach all 5 going north!

@drewphish
Missouri can go south to enter all of its 8 bordering states. Surprisingly Oklahoma is challenging and I think you have to go through Arkansas where the border has a gentle slope. But I can't tell which way the Oklahoma Missouri border itself slants. Iowa can be entered directly at a few points where the des moines river meanders