The Good, Bad, and Ugly Shootout

16.07.2018 |

Episode #2 of the course The world’s most compelling logic puzzles by John Robin


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.

See the Answer


Recommended resource

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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