# What a Freeway Interchange

There are six stalled cars on this complicated freeway interchange.

What is the maximum number of cars you can avoid, while entering and exiting the freeway where indicated by arrows?

Note: No sharp turns allowed!

Source: 1993 B. & P. Publishing Co., Inc.

• Those cars aren't stalled. They're pulled over scratching their heads looking at the map, wondering what insane urban planner designed this interchange... May 12, 2020 at 18:54
• What about backing up and reversing? It's then trivial to avoid them all. May 12, 2020 at 19:49
• Aside - Does this qualify as an interchange? there's only one road (okay two one-way roads) May 12, 2020 at 22:03
• Isn't it obvious from the first glance that you can avoid at least five (going counter clockwise along the outer rim), and the real question is if you can avoid all six? May 13, 2020 at 9:37
• @AndrewSavinykh yes obvious but i did not want to change the original since this is not mine.
– Oray
May 13, 2020 at 10:19

## 2 Answers

@Kralc's answer is correct, but to add a little to it...

Let's try to complete the route without passing any cars and see if that is possible. First, exclude all sections of the route that must involve passing a stalled car (marked in red):

Next, without encountering these red sections, draw lines that lead from the entrance and the exit as far as you can go without having to make any decisions about turn-offs (forgive the swerve in the car's path in the top-right of the diagram - I think an animal must have run out in front of me...):

Finally, note that if avoiding red routes and intersections with intermediate parts of the route leading from the entrance, the path of the line drawn from the exit can be forced until it meets the end of the other line:

Thus:

It is indeed possible to draw a line from the entrance to the exit without encountering a single other car!

• Just to add another point if view, you could also.. rot13(tbvat onpxjneqf. Gung jvyy gnxr lbh cerggl sne. Gjb fcyvg ebnqf bayl. Ohg vg'f rnfl gb frr juvpu jnl gb pubbfr) May 12, 2020 at 11:55
• @Prim3numbah Indeed - 'more than one way to skin a cat!' :)
– Stiv
May 12, 2020 at 11:57
• As an interim step - if you used Green and Blue instead of just Green, then it becomes easier to tell when one branch at a fork will just lead to a loop May 13, 2020 at 8:59
• @Chronocidal True - in hindsight, it would have been better to use different colours for the different ends (I will note that for the future), but hopefully it's not too confusing as it stands...
– Stiv
May 13, 2020 at 9:01

You can avoid ...

all of them: (assuming no other backed-up traffic!)