When we drive somewhere, we want to take the shortest route possible so that we can save money, gas, and time. The table below shows four cities and the distances between them.

Distances in miles between cities

 Distance Junky Junction Tvton Kooky Kounty Vanillaville Junky Junction 120 250 175 Tvton 120 100 190 Kooky Kounty 250 100 75 Vanillaville 175 190 75

John and Judy have to go  from Vanillaville to Tvton and Kooky Kounty for some work. They will stop for some parts for their computer in Junky Junction. After that, they will go back home. What is the shortest route (or routes) for their trip?

VV = Vanillaville
KK = Kooky Kounty
TT = Tvton
JJ = Junky Junction

VV-KK-TT-JJ-VV
75 + 100 + 120 + 175 = 470

VV-KK-JJ-TT-VV
75 + 250 + 120 + 190 = 635

VV-TT-KK-JJ-VV
190 + 100 + 250 + 175 = 715

VV-TT-JJ-KK-VV
190 + 120 + 250 + 75 = 635

VV-JJ-TT-KK-VV
175 + 120 + 100 + 75 = 470

VV-JJ-KK-TT-VV
175 + 250 + 100 + 190 = 715

The shortest route is from Vanillaville to Kooky County to Tvton to Junky Junction and back to Vanillaville and from Vanillaville to Junky Junction to Tvton to Kooky Kounty and back is 470 miles.

What is the shortest route (or routes) to go to all of the cities shown in the table below?

 A B C D A 200 540 430 B 200 400 410 C 540 400 290 D 430 410 290

ABCDA

ABDCA

ACBDA