Timing a stoplight just right

This Riddler is about how to perfectly time a stoplight, something we’ve all had to deal with!

You are driving your car on a perfectly flat, straight road. You are the only one on the road and you can see anything ahead of you perfectly. At time t=0, you are at Point A, cruising along at a speed of 100 kilometers per hour, which is the speed limit for the whole road. You want to reach Point C, exactly 4 kilometers ahead, in the shortest time possible. But, at Point B, 2 kilometers ahead of you, there is a traffic light.

At time t=0, the light is green, but you don’t know how long it has been green. You do know that at the beginning of each second, there is a 1 percent chance that the light will turn yellow. Once it turns yellow, it remains yellow for 5 seconds and then turns red for 20 seconds. Your car can accelerate or decelerate at a maximum rate of 2 meters per second-squared. You must always drive at or below the speed limit. You can pass through the intersection when the traffic light is yellow, but not when it is red.

What is the best strategy to reach your destination as soon as possible?

Here is my solution:
[Show Solution]

Non-intersecting chessboard paths

This Riddler classic puzzle is about finding non-intersecting paths on a chessboard:

First, how long is the longest path a knight can travel on a standard 8-by-8 board without letting the path intersect itself?

Second, there are unorthodox chess pieces that don’t exist in the standard game, which are known as fairy chess pieces. What are the longest nonintersecting paths that can be taken by the camel (which moves like a knight, except 3 squares by 1 square), the zebra (3 by 2), and the giraffe (4 by 1)?

This is a very challenging problem, and there doesn’t appear to be any way to solve it via some clever observation or simplification. Of course, we can try to come up with ever longer tours by hand, but we’ll never know for sure that we have found the longest one.

Much like the recent Pokemon Go problem, we must resort to computational means to obtain a solution. In this case, however, the problem is “small enough” that we can find exact solutions!

Here are some optimal tours:
[Show Solution]

If you’re interested in the details of how I found my solutions, read on:
[Show Solution]