Update Saturday 1am: I am not totally satisfied with this puzzle as it feels a bit contrived. I think I can make it both more realistic and not that much more convoluted. I am going to try to do that and repost within a couple weeks. However, I will not retract my $20 offer, as I do not want to cause anyone’s Friday night to have been spent in vain.
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You are in a city with a grid-based system of streets. You need to walk to a destination separated from you by N East/West streets and M North/South streets. There is a stoplight at every intersection. Each time you arrive at an intersection, there is
a) a 40% chance you can cross the North/South street with no wait, but that you’d have to wait 1 minute to cross the East/West street
b) a 40% chance you can cross the East/West street with no wait, but that you’d have to wait a minute to cross the North/South street
c) a 20% chance you can cross the street of your choosing, but that once you cross that street, you’d have to wait a minute to cross the street in the other direction
In a and b (as well as c), after you cross in one direction, you’d have to wait 1 minute before crossing in the other direction (this not a perfectly realistic model of how it works in the real world, since it takes time to cross the street, but it is the assumption for this puzzle), otherwise you can continue walking in the same direction to the next crossing (assuming that will get you closer to the destination).
By assumption it takes 2 minutes to walk the distance between any 2 adjacent streets, and it takes no time to actually cross a street.
If you follow the optimal strategy, what is the expected time it will take you to reach your destination?
$20 to the first person who provides the correct solution.
Maximum payout to any individual person for puzzle answers is $20.