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You're heading out to pick up your partner in crime's little sister from the train station. You're nearly there: between you and the train station is a small square of blocks, with 5 North-South streets, 5 East-West streets, and a total of 25 intersections. You're at the South West corner and the train station is accessed from the North East corner.

There's one problem: According to a magic device from your friend's uncle, there are about four drunken bandits in the way.

The bandits will likely be looking to steal your stylish skirt, so you'll have to avoid them. The bandits appear to be walking about randomly, at the same speed you can walk. You cannot tell where they are exactly. The bandits can see both directions down their current street, and all four directions at intersections. The buildings prevent them from seeing at diagonals. If they see you they'll break out into a run, where they'll move at twice your speed. You, however, cannot run.

While chasing you a bandit will run directly towards you if you run away from them, and will run to where they last saw you if you leave their line of sight. If you are visible from that point they will continue chasing, otherwise they'll get confused and return to randomly roaming.

When a bandit reaches you, they'll attack and take your skirt. However, if there's no other bandit who can see you then you can fight back, knocking out the bandit. A knocked-out bandit will no longer do anything. On the other hand, if another bandit sees you fighting back you'll be reported to the police and executed, meaning you'd have to let the bandit take your skirt.

Is there a strategy that can guarantee that you can reach the train station without losing your skirt?

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  • $\begingroup$ You cannot tell where they are exactly.- Does this imply that I will have a rough idea about where they are? like to the north/south/east/west of me? Or does that mean I just know there are 4 bandits? $\endgroup$
    – Pumpkin_Star
    Commented Feb 12 at 5:17
  • $\begingroup$ Also, can 2 bandits appear on a new road at the same time? $\endgroup$
    – Pumpkin_Star
    Commented Feb 12 at 5:19
  • $\begingroup$ So is the starting and ending points outside of the grid of roads?? $\endgroup$
    – PDT
    Commented Feb 12 at 12:25
  • $\begingroup$ @Pumpkin_Star you only know there are 4 bandits (no location information), and I don't know what you mean by your second question $\endgroup$
    – Ichthys King
    Commented Feb 12 at 12:46
  • $\begingroup$ Ok. And by the second question, what I mean is that- say I am approaching an intersection via a north-south road. Is it possible that two or more bandits approach the same intersection via the east-west roads? $\endgroup$
    – Pumpkin_Star
    Commented Feb 12 at 13:41

1 Answer 1

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Is there a strategy that can guarantee that you can reach the train station without losing your skirt?

No.

Let's label the North-South streets with a,b,c,d,e, starting from the west, and label de East-West streets with 1,2,3,4,5, starting from the south. (so we start at a1 and need to go at e5

Then

If the bandits are at the position a2, a3 and b1, c1 we cannot escape: No matter where we run, two of them will see us at any point, so we cannot fight back. We cannot run from the bandits, as both way out (north and east) are where the bandits are.

So

Sadly we cannot guarantee that our skirt will be safe.

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