The Good, Bad, and Ugly Shootout
Welcome back to your tour through the world of logic puzzles!
Today, I’d like to turn to a puzzle that combines visuals with mathematical reasoning. It goes like this: Good, Bad, and Ugly are about to take part in a three-way gunfight. Each is positioned on one of three points of a triangle. The rules:
1. Ugly will shoot first.
2. Bad will shoot second.
3. Good will shoot third.
4. After Good shoots, Ugly will shoot again, and they will continue steps 1-3 until only one person is left.
Some important facts:
• Ugly is the worst shot and can hit a target only one time in three.
• Bad is better, hitting a target two times in three.
• Good is the best, never missing.
You can assume everyone adopts the best strategy at each shot, so no one takes a bullet that isn’t meant for them (i.e., Good will always fire at Bad, since Ugly has less chance of hitting him; Bad will always fire at Good, since Good will kill him if he gets a shot, and when there are only two left standing, they will enter a duel).
Whom should Ugly aim at to have the best chance of surviving?
Work it out on your own first, then click the button below to find out if you’re right.
A thread of open-source solutions on this particular puzzle, which will show you some of the math, but also that the considerations are actually quite in-depth!
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